A rock is thrown horizontally from a bridge with a speed of 30.3 m/s. If the rock is 27.2 meters above the river at the moment of release, a)how long the rock is in the air? b)what is the horizontal distance to the point of impact from the point of release? c)what is the speed with which the rock strikes the river?
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To answer these questions, we can use the basic principles of projectile motion. Let's break down each part:
a) How long is the rock in the air?
In this case, since the rock is thrown horizontally, the vertical component of its initial velocity is zero. We can use the equation for vertical motion under constant acceleration to find the time of flight.
The equation we use is:
Δy = V0y * t + (1/2) * g * t^2
Where:
Δy is the vertical displacement (27.2 meters)
V0y is the vertical component of the initial velocity (which is zero in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time of flight
Rearranging the equation, we get:
(1/2) * g * t^2 = Δy
Substituting the given values, we have:
(1/2) * 9.8 * t^2 = 27.2
Now, solve for t:
4.9 * t^2 = 27.2
t^2 = 27.2 / 4.9
t ≈ √(5.55)
t ≈ 2.36 seconds
Therefore, the rock is in the air for approximately 2.36 seconds.
b) What is the horizontal distance to the point of impact from the point of release?
Since the rock is thrown horizontally, its horizontal velocity remains constant throughout the motion. We can use the formula: distance = speed * time.
Given:
Speed = 30.3 m/s
Time of flight = 2.36 seconds (from part a)
Horizontal distance = 30.3 m/s * 2.36 s
Horizontal distance ≈ 71.47 meters
Therefore, the horizontal distance to the point of impact from the point of release is approximately 71.47 meters.
c) What is the speed with which the rock strikes the river?
To find the velocity at which the rock strikes the river, we can use the equation for horizontal motion:
velocity = initial velocity = 30.3 m/s
Since there is no acceleration in the horizontal direction, the horizontal velocity remains constant. Therefore, the speed with which the rock strikes the river is 30.3 m/s.