A rock, mass = 2.0 kg, is fired straight up at 60 m/s from a catapult. What will be its maximum height at the moment it stops going up and starts to come down? Use the magnitude of g to be -10m/s2.
To find the maximum height reached by the rock, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
In this case, the rock is fired straight up, so the initial velocity (u) is 60 m/s and the final velocity (v) at the maximum height is 0 m/s since the rock stops going up and starts to come down.
We can rearrange the equation to solve for the displacement (s):
s = (v^2 - u^2) / (2a)
Substituting the given values:
s = (0^2 - 60^2) / (2 * -10)
s = (-3600) / (-20)
s = 180 meters
The maximum height reached by the rock is 180 meters.
To find the maximum height reached by the rock, we can use the equations of motion. We know the initial velocity (u) and acceleration (g) of the rock. Let's break down the problem into steps:
Step 1: Determine the time taken to reach maximum height (T).
We can use the equation: v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
At maximum height, the final velocity will be zero. Therefore, v = 0.
Rearranging the equation gives us: t = (v - u) / g.
Given:
u = 60 m/s (initial velocity)
g = -10 m/s^2 (acceleration due to gravity)
Substituting the values, we get:
t = (0 - 60) / -10
t = 6 seconds
Step 2: Calculate the maximum height (H).
To find the maximum height, we need to determine the distance traveled by the rock during the time it reaches maximum height.
We can use the equation: H = ut + (1/2)gt^2, where H is the maximum height.
Substituting the values, we get:
H = (60 * 6) + (1/2) * (-10) * (6^2)
H = 360 + (-180)
H = 180 meters
Therefore, the maximum height reached by the rock is 180 meters.
Use the potential energy and momentum.
mommentum = mass times velocity
So 2kg x 60m/s
Take that answer and set it equal to the formula for potential energy. This works because when the rocks velocity is zero all the energy will be converted from kinetic energy to potential energy.
So 2kg x 60m/s= 2kg x gravity x h.
And your height will be the moment it is at the absolute top of its height.