Question:
A ball of mass 100g is thrown vertically upward with an initial speed of 72 km/hr. Calculate:
(a) time taken for ball to return to the thrower:
1. Make sure that the units of measurements are the same. Notice that the question gives initial speed as 72 km/hr.
Convert that to meters/second
where:
1 km = 1000 m and
1 hour = 60 minutes and
1 minute = 60 seconds
Therefore:
72 km = 72 x 1000 m = 72 000 m
1 hour = 60 minutes x 60 seconds = 3600 seconds
=> 72 km / hr = 72000/3600 m/s = 20 m/s
=> Initial speed, U = 20 m/s
2. Recall that acceleration is the rate of change of velocity.
=> acceleration = (change in velocity) / time
In this case, when the ball reaches the maximum height, the final velocity is ZERO. => 0 m/s
And the acceleration is acceleration due to gravity ~ 10 m/s/s (seconds square)
So change in velocity is from 20 to zero = 20
acceleration = 10
plug these values into the formula above to get
10 = 20 / t
t = 20/10 = 2 seconds.
So the ball took 2 seconds to reach the maximum height where it's velocity is 0 m/s
It will take ANOTHER 2 seconds to reach back to thrower.
Therefore, time to reach back thrower will be 2 + 2 = 4 seconds.
(b) the maximum height reached:
1. Maximum height reached is area under velocity time graph. Which is the area of the triangle.
maximum height = (20 m/s X 2 s) / 2 = 20 meters
(c) gravitational potential energy when ball is half way up?
When ball is half way up, height = 20/2 = 10 meters
PE = mass X gravitational field strength X height,
Where:
mass is given as 100g and gravitational field strength is 10 N/kg. Notice that the mass is given in grams. But the gravitational field strength is in newtons per kg. So convert 100g to kg = 0.1 kg
Using the formula PE = mgh
PE = 0.1 x 10 x 10 = 10 J
(d) Kinetic energy when ball is half way down.
First, let's find out the potential energy when ball reaches maximum height (which is 20 meters)
PE = mgh = 0.1 x 10 x 20 = 20 J
Recall that at the maximum height, velocity is ZERO therefore ZERO kinetic energy too!
At the maximum height, all the energy is potential energy.
And recall the Law of Conservation of Energy. Where total energy should remains the same and they can only be converted from one form to another.
So.... When the ball is half way down, the potential energy IS THE SAME as when the ball is half way up which is 10 J
Therefore, kinetic energy half way down = Maximum PE - PE half way down = 20 - 10 = 10 J
ALTERNATIVELY:
Calculate using the kinetic energy formula
KE = 1/2 x m x v2
Where the kinematics formula to find velocity using acceleration and displacement is
v2 = u2 + 2as
v2 = (20)2 + 2(-10)(10)
*** noted a = -10 because we are taking upwards direction (initial velocity direction) as positive. So a downwards g will be negative ***
v2 = 400 - 200
v2 = 200
Put into the kinetic energy formula:
KE = 1/2 x 0.1 x 200 = 10 J
