A projectile is thrown with a velocity of 50 m/s at an angle of 53 wit...
Incorrect Statement: The projectile will reach a maximum height of 50 meters.
Explanation:
Projectile Motion: Projectile motion is the motion of an object thrown or projected into the air subject to the force of gravity. The motion of a projectile can be analyzed by resolving its initial velocity into horizontal and vertical components.
Given: The projectile is thrown with a velocity of 50 m/s at an angle of 53 with the horizontal.
Analysis: Let's analyze the motion of the projectile in two dimensions, horizontal and vertical.
Horizontal Motion: The horizontal motion of the projectile is uniform and is not affected by gravity. The horizontal velocity of the projectile can be calculated using the following formula:
vx = v cos θ
where vx is the horizontal component of velocity, v is the initial velocity of the projectile and θ is the angle of projection.
Substituting the given values, we get:
vx = 50 cos 53
vx = 27.76 m/s
Vertical Motion: The vertical motion of the projectile is affected by gravity. The vertical velocity of the projectile changes continuously due to the force of gravity. The vertical velocity of the projectile can be calculated using the following formula:
vy = v sin θ - gt
where vy is the vertical component of velocity, g is the acceleration due to gravity (9.8 m/s^2) and t is the time.
At the highest point of the projectile, the vertical velocity becomes zero. We can calculate the time taken by the projectile to reach the highest point using the following formula:
t = vy / g
Substituting the given values, we get:
t = 50 sin 53 / 9.8
t = 5.1 s
The maximum height reached by the projectile can be calculated using the following formula:
h = vy^2 / 2g
Substituting the given values, we get:
h = (50 sin 53)^2 / (2 x 9.8)
h = 65.3 m
Conclusion: Therefore, the incorrect statement is that the projectile will reach a maximum height of 50 meters. The correct maximum height reached by the projectile is 65.3 meters.
A projectile is thrown with a velocity of 50 m/s at an angle of 53 wit...
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