Yoko threw a stone upward at a speed of 10m/sec while standing on a cliff 40 m above ground.
A. What was the height of the stone after 3 seconds?
B. Estimate how long it took for the stone to touch the ground
v = Vi - g t
h = hi + Vi t - 4.9 t^2
after 3 seconds
h = 40 + 10 (3) - 4.9*9
= 25.9 meters above ground on the way down
0 = 40 + 10 t - 4.9 t^2
4.9 t^2 - 10 t - 40 = 0
t = [ 10 +/- sqrt(100 +784) ] / 9.8
take big t choice (on the way down)
t = 4.05 seconds
To solve these questions, we need to use the equations of motion under constant acceleration. Let's break it down step by step:
A. What was the height of the stone after 3 seconds?
We need to find the height of the stone after a given time. In this case, we are given the initial velocity (upward) and the height from the base. The equation we can use is:
h = initial height + (initial velocity * time) - (0.5 * gravity * time^2)
Where:
h = final height
initial height = 40 m (since Yoko is standing on a cliff)
initial velocity = 10 m/s (upward)
time = 3 s
gravity = 9.8 m/s^2 (acceleration due to gravity)
Substituting the given values into the equation, we have:
h = 40 + (10 * 3) - (0.5 * 9.8 * 3^2)
Calculating further:
h = 40 + 30 - 44.1
h = 25.9 m
Therefore, the height of the stone after 3 seconds is approximately 25.9 meters.
B. Estimate how long it took for the stone to touch the ground.
To estimate the time it takes for the stone to touch the ground, we can use the equation determining the time of flight:
time = (final velocity - initial velocity) / gravity
Since we know the initial velocity (10 m/s) and the acceleration due to gravity (9.8 m/s^2), we need to find the final velocity to calculate the time.
The final velocity can be determined using the equation:
final velocity = initial velocity - (gravity * time)
Since the stone reaches the maximum height at its peak, the final velocity at its highest point is 0 m/s. Therefore, we can solve for time.
0 = 10 - (9.8 * time)
Rearranging the equation:
9.8 * time = 10
Solving for time:
time = 10 / 9.8
Calculating further:
time ≈ 1.02 s
Therefore, it will take approximately 1.02 seconds for the stone to touch the ground.