Question

A unique type of basketball is played on the planet zarth. During the game, a player flies above the basket and drops the ball in from a height of 10 m. If the ball takes 5.0 s to fall, find the acceleration due to gravity on zarth.

Answer 1

The acceleration due to gravity on zarth = 0.8
`m/s^2`

Step-by-step explanation:

The acceleration due to gravity on earth = 9.8
`m/s^2`

We know that time taken(t) by an object to fall a distance (d) is given by

t =
`√( (2d/g))`

We are given the height from which the ball is dropped = 10m and the time taken by the ball to fall = 5.0s

So, substituting the given values

d = height of dropping the ball = 10m, t = 5.0 s

i.e. time taken for fall ,in the equation,

`t^2 = 2d/g`

`g= 20/5^2 = 20/25 = 0.8`

Therefore (g) = 0.8
`m/s^2` which gives the acceleration due to gravity on planet Zarth.

Answer 2

`0.8 m/s^2`

Step-by-step explanation:

The motion of an object in free fall is a uniformly accelerated motion, so we can analyze it using the following suvat equation:

`s=ut+(1)/(2)gt^2`

where, taking downward as positive direction:

s is the vertical displacement

u is the initial velocity

t is the time of flight

g is the acceleration of gravity

For the ball dropped in this problem,

s = 10 m

t = 5.0 s

u = 0

Therefore, solving the equation for g, we find the acceleration due to gravity:

`g=(2s)/(t^2)=(2(10))/(5^2)=0.8 m/s^2`