Question

A ball is kicked horizontally from the top of a 150 meter tall building. The ball lands 200m from the base of the building. what is the initial Velocity in the Horizontal direction?
positive
negative
scalar ​

Answer 1

The initial velocity in the horizontal direction will be positive.

Answer: Option A

Explanation:

As the ball threw off the building, the ball will follow a projectile path with free fall. So the velocity components will split as horizontal and the vertical velocity. The horizontal components of velocity remain same but the vertical velocities vary at rate of 9.8 m/s (approx. 10 m/s) as the ball will be reaching the ground due to free fall.

So gravity will act upon the ball leading to exhibit acceleration due to gravity will falling. Thus with the help of second equation of motion, we can determine the time taken by the ball to reach the ground from a height of 150 m. As the second equation of motion is

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

As the initial velocity of the ball before thrown is zero, u = 0 and as the ball is exhibiting a free fall, so acceleration a will be equal to acceleration due to gravity g. And the displacement performed by the ball will equal to height of the building.

Thus,

                    $150=(0 \times t)+\left(\frac{1}{2} \times g \times t^{2}\right)$

                    $150=\left(\frac{1}{2} \times 10 \times t^{2}\right)$

                    $t^{2}=\frac{150 \times 2}{10}=30$

Thus, the time taken for crossing the cliff is t = 5.5 s.

Now the distance at which the ball falls far from the base of the building is given as 200 m. So the horizontal velocity with which the ball is thrown can be found as,

                    $\text {Horizontal velocity}=\frac{\text {Distance}}{\text {Time}}=36.36 \mathrm{m} / \mathrm{s}$

Thus, the horizontal velocity is positive.