Help Free fall, looking for time of motion off of a bridge.

In summary, a person standing on a bridge throws a ball upward with an initial velocity of 23 m/s straight upwards. After 5.0 seconds, the ball will be at a displacement of -7.5 m. To find the time it takes for the ball to hit the water 10m below the release point, we can use the same equation for displacement and solve for time. Lastly, we can use conservation of energy to find the velocity of the ball when it reaches the water.
  • #1
cassiek
4
0
Help! Free fall, looking for time of motion off of a bridge.

Homework Statement


A person standing on a bridge throws a ball upward with an initial velocity of 23 m/s straight upwards so if it comes back down it will just pass the edge of the bridge and keep going down.
a) where will the ball be after 5.0s?
b) how long will it take to hit the water if the water 10m below the ball's release point?
c) what velocity will the ball have when it reaches the water?

Homework Equations


The kinematics equations of motion.

The Attempt at a Solution


for a) I used the equation Δd = vΔt + 1/2aΔt² (where d is displacement, v is the initial velocity, a is acceleration due to gravity, and t is the time) and I solved for d. I got -7.5 m. I'm hoping this is correct!
I don't know how to tackle b) and c) though, so advice is GREATLY APPRECIATED!
 
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  • #2


when ball is going upwards, a = -g, and when it is coming downwards, a = g, g = 9.8 m/s^2
 
  • #3


and yes, Welcome to PF cassiek!
 
  • #4


cassiek said:
Help! Free fall, looking for time of motion off of a bridge.

Seems you were falling off the bridge.

Use the same equation for b part. This time you have displacement but not time.
use conservation of energy for the third part.
 
  • #5


Hello! I can definitely help you with this problem. For part b), we can use the same equation you used for part a) but solve for t instead. So the equation would be t = (vf - vi)/a, where vf is the final velocity (which would be 0 when the ball hits the water), vi is the initial velocity (23 m/s), and a is the acceleration due to gravity (-9.8 m/s²). Plugging in these values, we get t = 2.35 seconds. This is the time it takes for the ball to hit the water.

For part c), we can use the equation vf = vi + at, where vf is the final velocity (which we are looking for), vi is the initial velocity (23 m/s), a is the acceleration due to gravity (-9.8 m/s²), and t is the time it takes for the ball to hit the water (which we found in part b)). Plugging in these values, we get vf = 23 - 9.8(2.35) = 0 m/s. So the velocity of the ball when it reaches the water is 0 m/s, which makes sense since it has stopped moving at that point.

I hope this helps! Let me know if you have any other questions.
 

1. How do you calculate the time of motion for free fall off a bridge?

To calculate the time of motion for free fall off a bridge, you can use the equation t = √(2h/g), where "t" is the time, "h" is the height of the bridge, and "g" is the acceleration due to gravity (9.8 m/s²). This equation assumes that the object is dropped from rest and neglects air resistance.

2. What is the acceleration due to gravity?

The acceleration due to gravity, denoted by "g", is a constant value of 9.8 m/s² near the Earth's surface. This value represents the rate of change of an object's velocity as it falls towards the Earth due to the force of gravity.

3. Does the mass of an object affect its free fall time?

No, the mass of an object does not affect its free fall time. According to the equation t = √(2h/g), only the height of the bridge and the acceleration due to gravity are factors in calculating the free fall time. The mass of the object does not play a role in this equation.

4. How does air resistance impact the time of motion for free fall off a bridge?

Air resistance, also known as drag, can affect the time of motion for free fall off a bridge. As an object falls, it experiences an upward force from air resistance that opposes its downward motion due to gravity. This can slow down the object and increase its fall time, but the impact may be negligible for most objects.

5. Is there a maximum height for free fall off a bridge?

Technically, there is no maximum height for free fall off a bridge as long as the object has sufficient time to reach terminal velocity, which is when the force of air resistance equals the force of gravity. However, for practical purposes, the height of the bridge should be within a safe range where the impact of the fall will not cause harm to the object or surroundings.

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