Multiple part question…..
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0m above a flat, horizontal beach. With what angle of impact does the stone land (in degrees).
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18 m/s. the cliff is 50 m above a flat, horizontally beach. how long after being released does the stone strike the beach below the cliff?
A student atands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above flat, horizontal beach. With what speed of impact does the stone land?
The horizontal velocity component remains
Vx = 18.0 m/s
during the fall to the beach.
The vertical component of velocity (measured positive upwards) is
Vy = - gt
The time t that it takes to reach the beach when falling from height H is given by solving
H = (g/2) t^2
Therefore t = sqrt (2H/g) = 3.19 s
That answers your second question. Use that value of t to compute Vy at impact and from that and Vx get the angle of impact.
The speed of impact is sqrt[Vx^2 + Vy^2]
To answer these questions, we will use the concept of projectile motion. The key idea is that the horizontal and vertical motions of the thrown stone are independent of each other.
1. Angle of Impact:
To find the angle of impact at which the stone lands, we need to determine the time it takes for the stone to fall vertically and the horizontal distance traveled during that time.
The vertical distance traveled is given by the height of the cliff, which is 50.0m. We can use the formula for free fall motion:
h = (1/2) * g * t^2,
where h is the vertical distance, g is the acceleration due to gravity (approximately 9.8m/s^2), and t is the time of flight.
Simplifying the equation, we get:
t = sqrt((2 * h) / g).
The horizontal distance traveled is given by the formula:
d = v * t,
where v is the initial horizontal velocity of the stone (which is equal to 18.0m/s) and t is the time of flight.
Now, we can find the angle of impact using the inverse tangent function:
theta = atan(d / h).
2. Time of Impact:
To find the time it takes for the stone to strike the beach below the cliff, we only need to consider the vertical motion of the stone. The horizontal velocity does not affect the time of impact for a projectile thrown horizontally.
Using the same formula for vertical motion as mentioned above, we can calculate the time:
t = sqrt((2 * h) / g).
3. Speed of Impact:
To find the speed of impact at which the stone lands, we need to calculate the total velocity of the stone just before it hits the ground. The horizontal velocity remains constant throughout the motion (18.0m/s), and the vertical velocity increases due to the effect of gravity.
We can use the formula for the final velocity in free fall motion:
v^2 = u^2 + 2gh,
where v is the final velocity, u is the initial vertical velocity (0m/s), g is the acceleration due to gravity, and h is the height of the cliff.
Simplifying the equation, we get:
v = sqrt(2 * g * h).
Now, you can plug in the given values and solve these equations to find the angle of impact, time of impact, and speed of impact.