Question

A ball with a horizontal speed of 1.25ms−1 rolls off a bench 1.00m above the floor.a. How long will it take the ball to hit the floor?b. How far from a point on the floor directly below the edge of the bench will the ball land?

Answer 1

a) Time taken to hit the ground = 0.45 sec

b) The ball will land at 0.56 m from the table.

Step-by-step explanation:

The ball travels a vertical distance y=1 m and horizontal distance x i-e

Vertical distance =y = 1 m

Horizontal distance = x= ?

(see diagram file attached)

To find value of x we need time taken to travel this distance. When time is known then we can use

x= Vx × t r elation to find distance x

To find time we consider vertical motion only.

So, Vertical distance =y= 1 m

Gravitational acceleration = g = 9.8 m/sec2

Initial vertical velocity = Vyi =0 m/sec

Using formula

y=Vyi t + 1/2 g
`t^(2)`

==> 1= o+ 1/2 ×9.8×
`t^(2)`

==> 1=4.9 ×
`t^(2)`

`t^(2)`= 1/4.9= 0.204081633

==> t = 0.45 sec

This is the time for vertical distance

-- but this will also be the time to travel horizontal distance x

So for horizontal distance use

x= Vx× t

Here

Vx = 1.25 m/sec

t= 0.45 sec

==> x= 1.25 × 0.45 = 0.56 m