Question

A stone is thrown from the top of a tower at an angle of 30 degree above the horizontal level with a velocity of 40 m/s . it strikes the ground after 5 seconds from the time of projection then the height of the tower is

Answer 1

Explanation:

your answer is in the above attachment

Answer 2

∴ The height of the tower is 25m.

Given:

Angle at which the stone is thrown = 30°

The initial velocity of stone = 40 m/s

Time taken for the stone to reach the ground = 5 seconds.

To Find:

The height of the tower.

Solution:

A stone is projected at an angle of 30° from the top of the building. The motion takes place along the y-axis and the path it follows is parabolic.

Acceleration due to gravity, g = -10 m/s²

The angle at which the stone is thrown, θ = 30°

Time taken for the stone to reach the ground, t = 5 seconds.

The initial velocity of the stone, u = 40 m/s

On resolving u along the x and y-axis, we get

The initial velocity along y-axis $u_{y }$ = u sinθ = u sin 30° = 20 m/s

From second equation of kinematics, we have

The displacement, s = ut + $\frac{1}{2}$ at²

Here displacement s = height of tower = -h  ( the negative sign arises on account of the motion of stone being in the  negative y-direction)

∴ -h = ut + $\frac{1}{2}$ at² = 20(5)+ $\frac{1}{2}$(-10)(5²) = -125 + 100 = -25

⇒ h = 25m

∴ The height of the tower is 25m.

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