Question

(Español) Una bola es lanzada verticalmente hacia abajo con una velocidad inicial de 15 m/s desde una altura de 50 m. (a) Determine la velocidad en el instante que golpea el suelo. (b) y el tiempo que toma en caer.

(English) A ball is thrown vertically downward with an initial velocity of 15 m / s from a height of 50 m. (a) Determine the velocity at the instant it hits the ground. (b) and the time it takes to fall.

Answer 1

Data given in the question are,

Initial velocity of ball = = 15 m/s

Height from which ball is thrown = = 50 m

Acceleration of the ball is the acceleration due to gravity.

So acceleration = = g = 9.8 m/s^2

Using kinematic formulas we can find the velocity with which the ball hits the ground and the time taken to fall on the ground.

To find the time taken to fall,

using the formula, ........(1)

where t = time taken to fall

Putting the values in equation(1), we get

  

..................................(2)

Now there are two values of t according to the sign considered. The negative sign will give a negative value of t and time cannot be negative. So only positive sign is taken for calculation.

So, from equation (2)

2.0115 s ................(3)

Now to calculate the velocity of the ball at the instant it hits the ground,

consider the kinematics formula, .......................(4)

Here is the final velocity of ball when it touches the ground.

So,

m/s ..................(5)

Hence, the velocity of the ball at the instant it hits the ground is 34.7127 m/s and the time taken for fall is 2.0115 s.