During the battle of Bunker Hill, Colonel William Prescott ordered the American Army to bombard the British Army camped near Boston. The projectiles had an initial velocity of 41 m/s at 38° above the horizon and an initial position that was 35 m higher than where they hit the ground. How far did the projectiles move horizontally before they hit the ground? Ignore air resistance.

Explanation:

Given:

height of the initial projection point above the ground,

Vertical component of the velocity:

The time taken in course of going up:

(at top the final velocity will be zero)

In course of going up the maximum height reached form the initial point:

(at top height the final velocity is zero. )

using eq. of motion,

where:

final vertical velocity while going up.=0

maximum height

Now the total height to be descended:

Now the time taken to fall the gross height in course of falling from the top:

Now the total time the projectile spends in the air:

Now the horizontal component of the initial velocity:

(it remains constant throughout the motion)

Therefore the horizontal distance covered in the total time;

Explanation:

initial velocity, u = 41 m/s

angle, θ = 38 °

height, h = 35 m

Let the time is t.

Use second equation of motion in vertical direction

h = ut + 1/2 gt²

- 35 = 41 Sin 38 t - 0.5 x 9.8 x t²

4.9t² - 25.2 t - 35 = 0

t = 6.3 second

Horizontal distance traveled in time t is

d = uCos 38 x t

d = 41 x Cos 38 x 6.3

d = 203.54 m

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