someone in a car going past you at the speed of 31m/s drops a small rock from a height of 1.5m.
So much for the scenario. What is the question?
To determine the time it takes for the rock to hit the ground, you can use the equations of motion. First, we need to find the time it takes for the rock to fall from a height of 1.5m.
We can use the equation of motion:
s = ut + (1/2)at^2
where:
s = displacement (1.5m)
u = initial velocity (0 m/s)
a = acceleration due to gravity (-9.8 m/s^2)
t = time
Rearranging the equation:
1.5 = (1/2)(-9.8)t^2
Multiplying both sides by 2 and dividing by -9.8:
t^2 = -0.306
Taking the square root of both sides:
t ≈ ±0.554s
Since time cannot be negative, we consider the positive value:
t ≈ 0.554s
Now, using the speed of the car (31 m/s), we can determine the horizontal distance the car travels during that time.
d = vt
where:
d = distance
v = velocity (31 m/s)
t = time (0.554s)
Substituting the values:
d = (31 m/s)(0.554s)
d ≈ 17.074m
Therefore, when the rock hits the ground, the car would have traveled approximately 17.074 meters.