Question

A monkey throws a coconut from a height of 4.0 m and with an initial speed of 3.5 m/sFind a) the time for the coconut to hit the ground, b) the distance the coconut landed from the base of the vertical cliff, c) the velocity of the coconut when it hit the ground.

Answer 1

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. We will start by finding the time through the position equation based on the initial velocity and acceleration (in this case gravity), then we will find the distance traveled through the function that relates it to time and velocity and finally We will find the rate of fall through the equations that relate to acceleration and position:

Our values are given as,

`h = 4m`

`v_x = 3.5m/s`

`v_y = 0`

PART A) From the first equation we have that,

`h = v_0t +(1)/(2)t^2`

There is not initial velocity, then

`t = \sqrt{(2h)/(g)}`

`t = \sqrt{(2(4))/(9.8)}`

`t = 0.9s`

PART B ) Distance from the base

`x = v_x t`

`x = (3.5)(0.9)`

`x = 3.15m`

PART C) Velocity of the coconut when it hits the ground

`v_y^2 = v_i^2+2gh`

`v_y = √(2gh)`

`v_y = √(2(9.8)(4))`

`v_y = 8.85m/s`