Julie throws a rock vertically upward. From a height of 64.0 meters above thehow ground. The initial velocity of the rock is 31.0 meters per second neglect air resistance
How long does it take for the rock to hit the ground?
What is the velocity of the rock just before it hit the ground?
h=v₀t+gt²/2,
gt²+2v₀t-2h=0
Solve for t.
v= v₀+gt
To find the time it takes for the rock to hit the ground, we can use the equation of motion for vertical motion:
s = ut + (1/2)at^2
where:
s = displacement (in this case, final displacement is 0 as the rock hits the ground)
u = initial velocity
t = time taken
Rearranging the equation, we get:
0 = ut - (1/2)gt^2
Since the only unknown in this equation is t, we can solve for t.
-16t^2 + 31t - 64 = 0
Solving this quadratic equation, we get two possible values for t. However, the negative value can be ignored as time cannot be negative in this case.
Now, let's find the velocity of the rock just before it hits the ground.
We can use another equation of motion:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration (in this case, acceleration due to gravity)
To find the acceleration, we can use the equation:
a = g
where g is the acceleration due to gravity which is approximately -9.8 m/s^2.
Now substitute the values into the equation to find the final velocity.