Someone in a car going past you at the speed of 35 m/s drops a small rock from a height of 1.5 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.
Answer in units of m.
Someone in a car going past you at the speed of 39 m/s drops a small rock from a height of 1.9 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
Well, let's calculate the time it takes for the rock to hit the ground. We can use the equation d = 1/2 * g * t^2, where d is the distance the rock falls, g is the acceleration due to gravity, and t is the time it takes for the rock to hit the ground.
Since the initial velocity of the rock is 0 m/s (it's just dropped), we can use the equation v = gt to find the time, where v is the final velocity (which is 0 m/s).
Rearranging the equation, we get t = v/g. Plugging in v = 0 m/s and g = 9.8 m/s^2, we find t = 0.
Oh no! It seems that I made a mistake. The rock should hit the ground immediately after it's dropped. So the distance the rock will travel horizontally is 0 meters. Sorry for the confusion, but don't worry, there won't be any need to dodge falling rocks!
To find the distance from the point of drop to where the rock hits the ground, we need to consider two factors: the horizontal motion of the car and the vertical motion of the rock.
First, let's calculate the time it takes for the rock to hit the ground. We can use the formula for the time of flight of an object in free fall:
t = sqrt((2 * h) / g)
where h is the initial height of the rock (1.5 m) and g is the acceleration due to gravity (9.8 m/s^2).
Plugging in the values, we get:
t = sqrt((2 * 1.5) / 9.8)
t ≈ 0.566 s
Now, let's calculate the horizontal distance traveled by the car during this time. The horizontal distance is given by:
d = v * t
where v is the speed of the car (35 m/s) and t is the time calculated above.
Plugging in the values, we get:
d = 35 * 0.566
d ≈ 19.81 m
Therefore, the rock will hit the ground approximately 19.81 meters from the point of the drop.
To calculate how far the rock will hit the ground, we need to find the time it takes for the rock to fall and the horizontal distance traveled by the car during that time.
First, let's determine the time it takes for the rock to fall. We can use the formula:
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 formula to solve for time:
t^2 = (2 * h) / g
t = sqrt((2 * h) / g)
Substituting the given values:
h = 1.5 m
g = 9.8 m/s^2
t = sqrt((2 * 1.5) / 9.8)
Calculating the value of t gives us:
t ≈ 0.509 s (rounded to three decimal places)
Now, we need to find the horizontal distance traveled by the car during this time. The distance can be calculated using the formula:
d = v * t
where d is the distance, v is the velocity of the car, and t is the time.
Substituting the given values:
v = 35 m/s
t = 0.509 s
d = 35 * 0.509
Calculating the value of d gives us:
d ≈ 17.815 m (rounded to three decimal places)
Therefore, the rock will hit the ground approximately 17.815 meters from the point of the drop.
Xo = 35 m/s.
h = 1.5 m.
h = 0.5g*t^2 = 1.5 m.
4.9t^2 = 1.5
t^2 = 0.306
Tf = 0.553 s. = Fall time.
Dx = Xo*Tf = 35m/s * 0.553s = 19.4 m.