Someone in a car going past you at the speed of 24 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/s2.
To find the horizontal distance from the point of the drop where the rock will hit the ground, we can use the formula for horizontal motion:
distance (d) = velocity (v) × time (t)
First, let's find the time it takes for the rock to hit the ground. To do this, we need to find the time it takes for the rock to fall from a height of 1.6 m.
Using the formula for vertical motion, we can calculate the time:
height (h) = initial velocity (u) × time (t) + 0.5 × acceleration (a) × time (t)^2
In this case, the height is 1.6 m, the initial velocity is 0 m/s (since it's dropped), and the acceleration is -9.8 m/s^2 (negative because it's acting against the direction of motion). We need to solve for time (t):
1.6 = 0 × t + 0.5 × (-9.8) × t^2
1.6 = -4.9t^2
t^2 = -1.6 / -4.9
t^2 = 0.32653
t = √(0.32653)
t ≈ 0.57 s
Now that we know the time it takes for the rock to fall, we can find the horizontal distance it travels during this time. The velocity of the car doesn't affect the vertical motion, so we can consider only the initial vertical velocity of the rock as 0 m/s.
d = v × t
= 24 m/s × 0.57 s
≈ 13.68 m
Therefore, the rock will hit the ground approximately 13.68 m from the point of the drop.
To find the distance from the point of the drop where the rock will hit the ground, we need to determine the time it takes for the rock to fall and then calculate the horizontal distance traveled by the car during that time.
Let's break down the problem into two components: vertical motion and horizontal motion.
1. Vertical Motion:
The rock is dropped from a height of 1.6 m, so its initial vertical velocity is zero (since it's dropped, not thrown). The only force acting on the rock is gravity, which causes its acceleration in the vertical direction to be -9.8 m/s^2 (negative because it acts downward). We can use the following formula to find the time it takes for the rock to fall:
h = (1/2) * g * t^2
Where h is the height, g is the acceleration due to gravity, and t is the time.
Rearranging the equation, we get:
t^2 = (2 * h) / g
t = sqrt((2 * h) / g)
Substituting the given values:
t = sqrt((2 * 1.6) / 9.8)
t ≈ sqrt(0.326)
t ≈ 0.57 seconds (rounded to two decimal places)
2. Horizontal Motion:
The car is traveling at a speed of 24 m/s. During the time it takes for the rock to fall, the car will continue moving at a constant velocity. The distance the car travels during this time is given by:
d = v * t
Substituting the given values:
d = 24 * 0.57
d ≈ 13.68 meters (rounded to two decimal places)
Therefore, the rock will hit the ground approximately 13.68 meters from the point of the drop.
time to fall to ground: h=gt t=h/g solve that.
distance horizontal=velocity*time=24*1.6/9.8 m