Someone in a car going past you at the
speed of 43 m/s drops a small rock from a
height of 1.6 m.
How far from the point of the drop will the
rock hit the ground? The acceleration due to
gravity is 9.8 m/s
2
.
Answer in units of m
To calculate the distance the rock will travel horizontally before hitting the ground, we can use the formula:
Horizontal distance = initial velocity * time
In this case, the initial velocity of the rock in the horizontal direction is the same as the car's velocity since the rock is dropped vertically.
The time it takes for the rock to hit the ground can be found using the following formula:
time = √(2 * height / gravity)
where height is the vertical distance the rock is dropped (1.6 m) and gravity is the acceleration due to gravity (9.8 m/s^2).
Plugging in the values,
time = √(2 * 1.6 / 9.8) = √0.3265 ≈ 0.57 s
Now, we can calculate the horizontal distance:
Horizontal distance = 43 m/s * 0.57 s ≈ 24.51 m
Therefore, the rock will hit the ground approximately 24.51 meters from the point of the drop.
To find the distance from the point of the drop where the rock will hit the ground, we can use the equations of motion. Since the rock is dropped from a height, we can assume that its initial velocity is 0 m/s.
Let's break down the problem and find a solution step by step:
1. Determine the time it takes for the rock to hit the ground.
We can use the equation:
s = ut + (1/2)at^2
Where:
s = distance (the height from where the rock is dropped)
u = initial velocity (0 m/s for a dropped object)
a = acceleration due to gravity (-9.8 m/s^2, taking downward as negative)
t = time
Rearranging the equation to solve for time (t):
t^2 = (2s)/a
t = √((2s)/a)
Substituting the given values:
t = √((2 * 1.6) / 9.8)
t ≈ 0.4984 seconds
2. Calculate the distance the car travels in that time.
The distance the car travels can be found using the equation:
d = ut
Where:
d = distance
u = velocity of the car (43 m/s)
t = time (0.4984 seconds)
Substituting the given values:
d = 43 * 0.4984
d ≈ 21.42 meters
Therefore, the rock will hit the ground approximately 21.42 meters from the point of the drop.
Note: It is important to consider that this calculation assumes there are no other factors influencing the motion of the rock, such as air resistance.
Vertical distance fallen = (g/2)*t^2
= 1.6 m
Solve for t.
Multiply what you get by 43 m/s.