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A stone is Thrown from the top of a tower at an angle of 30 degree up with the horizontal with a velocity of 16m/s . After 4s of flight it strikes the ground. Calculate the height of the tower from the ground and the horizontal range of the stone.?
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A stone is Thrown from the top of a tower at an angle of 30 degree up ...
Given data:
Angle of projection (θ) = 30°
Initial velocity (u) = 16 m/s
Time of flight (t) = 4 s

Calculating the height of the tower:
To calculate the height of the tower, we need to find the vertical component of the initial velocity (u) and the time taken to reach the ground (t).

The vertical component of velocity (v) can be calculated using the formula:
v = u * sin(θ)

Substituting the given values:
v = 16 * sin(30°)
v ≈ 8 m/s

The time taken to reach the ground is equal to the time of flight (t) which is given as 4 s.

Using the formula for vertical motion:
h = u * t + (1/2) * g * t^2

where h is the height, u is the initial velocity, t is the time taken, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values:
h = 8 * 4 + (1/2) * 9.8 * (4^2)
h = 32 + 78.4
h ≈ 110.4 m

Therefore, the height of the tower from the ground is approximately 110.4 meters.

Calculating the horizontal range:
To calculate the horizontal range, we need to find the horizontal component of the initial velocity (u) and the time taken to reach the ground (t).

The horizontal component of velocity (v) can be calculated using the formula:
v = u * cos(θ)

Substituting the given values:
v = 16 * cos(30°)
v ≈ 13.856 m/s

The time taken to reach the ground is equal to the time of flight (t) which is given as 4 s.

Using the formula for horizontal motion:
R = v * t

where R is the horizontal range, v is the horizontal component of velocity, and t is the time taken.

Substituting the values:
R = 13.856 * 4
R ≈ 55.424 m

Therefore, the horizontal range of the stone is approximately 55.424 meters.

Summary:
The height of the tower from the ground is approximately 110.4 meters and the horizontal range of the stone is approximately 55.424 meters.
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A stone is Thrown from the top of a tower at an angle of 30 degree up with the horizontal with a velocity of 16m/s . After 4s of flight it strikes the ground. Calculate the height of the tower from the ground and the horizontal range of the stone.?
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A stone is Thrown from the top of a tower at an angle of 30 degree up with the horizontal with a velocity of 16m/s . After 4s of flight it strikes the ground. Calculate the height of the tower from the ground and the horizontal range of the stone.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A stone is Thrown from the top of a tower at an angle of 30 degree up with the horizontal with a velocity of 16m/s . After 4s of flight it strikes the ground. Calculate the height of the tower from the ground and the horizontal range of the stone.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is Thrown from the top of a tower at an angle of 30 degree up with the horizontal with a velocity of 16m/s . After 4s of flight it strikes the ground. Calculate the height of the tower from the ground and the horizontal range of the stone.?.
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