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A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane?
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A projectile is thrown with belocity of 50m/stowards an inclined plane...
Let a be angle of projectile and b be angle of the inclined plane.
THE FORMULAE IS :
This is the distance along the plane and it is given by :
S = u Cos (a - b)
u is the initial speed.
Substituting we have :
= 50x Cos (53 - 45)
= 50 x Cos 8 = 49.51 m
This question is part of UPSC exam. View all JEE courses
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A projectile is thrown with belocity of 50m/stowards an inclined plane...
Time of Flight and Distance Calculation for Projectile Motion
Given Data:
- Initial velocity (u) = 50 m/s
- Angle of projection (θ) = 53 degrees
- Inclined plane angle (α) = 45 degrees
Time of Flight Calculation:
- The time of flight can be calculated using the formula:
Time of flight = 2 * (u * sin(θ)) / g
where g is the acceleration due to gravity (9.8 m/s^2)
- Substituting the given values, we get:
Time of flight = 2 * (50 * sin(53)) / 9.8
≈ 5.26 seconds
Distance Calculation:
- To find the horizontal distance between the point of projection and the foot of the inclined plane, we need to first calculate the horizontal and vertical components of the projectile motion.
- The horizontal component can be calculated as:
Horizontal component = u * cos(θ) * time of flight
Substituting the values, we get:
Horizontal component = 50 * cos(53) * 5.26
≈ 180.33 meters
- Next, we need to calculate the vertical component at the time of impact with the inclined plane. This can be determined using the formula:
Vertical component = u * sin(θ) * time of flight - 0.5 * g * t^2
where t is the time at which the projectile hits the inclined plane.
- Substituting the values, we get:
Vertical component = 50 * sin(53) * 5.26 - 0.5 * 9.8 * (5.26)^2
≈ 86.83 meters
- Finally, the distance between the point of projection and the foot of the inclined plane can be calculated using the Pythagorean theorem:
Distance = sqrt((Horizontal component)^2 + (Vertical component)^2)
≈ sqrt((180.33)^2 + (86.83)^2)
≈ 201.36 meters
Therefore, the time of flight for the projectile is approximately 5.26 seconds, and the distance between the point of projection and the foot of the inclined plane is approximately 201.36 meters.
Given Data:
- Initial velocity (u) = 50 m/s
- Angle of projection (θ) = 53 degrees
- Inclined plane angle (α) = 45 degrees
Time of Flight Calculation:
- The time of flight can be calculated using the formula:
Time of flight = 2 * (u * sin(θ)) / g
where g is the acceleration due to gravity (9.8 m/s^2)
- Substituting the given values, we get:
Time of flight = 2 * (50 * sin(53)) / 9.8
≈ 5.26 seconds
Distance Calculation:
- To find the horizontal distance between the point of projection and the foot of the inclined plane, we need to first calculate the horizontal and vertical components of the projectile motion.
- The horizontal component can be calculated as:
Horizontal component = u * cos(θ) * time of flight
Substituting the values, we get:
Horizontal component = 50 * cos(53) * 5.26
≈ 180.33 meters
- Next, we need to calculate the vertical component at the time of impact with the inclined plane. This can be determined using the formula:
Vertical component = u * sin(θ) * time of flight - 0.5 * g * t^2
where t is the time at which the projectile hits the inclined plane.
- Substituting the values, we get:
Vertical component = 50 * sin(53) * 5.26 - 0.5 * 9.8 * (5.26)^2
≈ 86.83 meters
- Finally, the distance between the point of projection and the foot of the inclined plane can be calculated using the Pythagorean theorem:
Distance = sqrt((Horizontal component)^2 + (Vertical component)^2)
≈ sqrt((180.33)^2 + (86.83)^2)
≈ 201.36 meters
Therefore, the time of flight for the projectile is approximately 5.26 seconds, and the distance between the point of projection and the foot of the inclined plane is approximately 201.36 meters.
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A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane?
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A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane?.
A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane?.
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A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane?, a detailed solution for A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? has been provided alongside types of A projectile is thrown with belocity of 50m/stowards an inclined plane from ground such that it strikes the inclined plane perpendicular. The angle of projection of projectile is 53 degree with the horizontal and inclined plane is inclined at an angle of 45 degree to horizontal.find the time of flight and the distance between the point of projection and the foot of inclined plane? theory, EduRev gives you an
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