Question

A ball rolls off a desk at a speed of 3.0 m/s and lands 0.40 seconds later.

a) how far from the base of the desk does the ball land
b) how high is the desk?
c) What is the speed of impact?

Answer 1

c) what is the speed of the impact

Answer 2

Part a)

`d = 1.2 m`

Part b)

`\Delta y = 0.78 m`

Part c)

`v = 4.9 m/s`

Step-by-step explanation:

Part a)

Speed of the ball = 3.0 m/s

time taken by the ball to hit the floor = 0.40 s

so the total distance moved by the ball in horizontal direction is given as

`d = velocity * time`

`d = (3.0)* 0.40`

`d = 1.2 m`

Part b)

The height of the desk is same as the displacement of ball in vertical direction during its free fall

so it is given as

`\Delta y = v_y t + (1)/(2)at^2`

`\Delta y = 0 + (1)/(2)(9.81)(0.40)^2`

`\Delta y = 0.78 m`

Part c)

In x direction the velocity of ball will remains the same

`v_x = 3.0 m/s`

in Y direction the velocity of ball is given as

`v_y = v_i + at`

`v_y = 0 + (9.81)(0.40)`

`v_y = 3.92 m/s`

so the speed of the ball is given as

`v = √(v_x^2 + v_y^2)`

`v = √(3.92^2 + 3.0^2)`

`v = 4.9 m/s`