A steel projectile is shot horizontally at 20m/s from the top of a 40m tower. How long does it take to hit the ground? How far f

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hoa

1 month ago

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A steel projectile is shot horizontally at 20m/s from the top of a 40m tower. How long does it take to hit the ground? How far f

rom the base of the tower does the projectile hit the ground

Physics

1 answer:

inna [3.1K] · Answer 1 · 2026-03-28T11:44:01+03:00

1) It takes 2.86 seconds

To determine the time of flight, we need to evaluate the stone's vertical motion, characterized by uniformly accelerating motion (free fall) where gravitational acceleration is constant.

The vertical position at time t is expressed as

$s=u t + \frac{1}{2}gt^2$

In this case, we define downward as the positive direction

$u$ as the initial vertical velocity (which is zero, given the projectile is launched horizontally)

t signifies the elapsed time

$g=9.8 m/s^2$ g indicates gravitational acceleration

In this scenario, we have

s = 40 m (vertical distance corresponds to the height of the tower)

By solving for t, we can determine the time of the projectile's flight:

$s=\frac{1}{2}gt^2\\t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(40)}{9.8}}=2.86 s$

Thus, the projectile takes 2.86 s to reach the ground.

2) Horizontal distance: 57.2 m

The projectile's horizontal motion is uniform; in fact, no forces affect it along that direction, rendering the horizontal acceleration zero, therefore, the horizontal velocity remains constant.

The initial horizontal velocity of the projectile is

$v_x = 20 m/s$

Consequently, to compute the horizontal distance traveled by the projectile, we can utilize the formula

$d=v_x t$

And by substituting the time of flight, we find out when the projectile impacts the ground:

t = 2.86 s

Thus, we derive:

$d=(20)(2.86)=57.2 m$