Height of pier above water- projectile motion

In summary, a swimmer moving at 1.80m/s dives off a pier and hits the water 0.80m from the edge of the pier. Using the equations dv=1/2*at2 and dh=Vh*Δt, the height of the pier above the water can be calculated to be 0.97m, with a time of 0.44s. These answers are correct and respect significant figures.
  • #1
dani123
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Homework Statement



A swimmer moving at 1.80m/s, dives off a pier and hits the water 0.80m from the edge of the pier. How high is the pier above the water?


Homework Equations



dv=1/2*at2
dh=Vh*Δt
a=9.8

The Attempt at a Solution



dh=0.80m
Vh=1.80m/s
dv=?
t=?

First started by solving for Δt in the dh=Vh*Δt equation and found that Δt=0.44s

Then I plugged it into the dv=1/2*at2 equation

dv=0.97m

I would like for someone to just verify that my answers are correct and the significant figures are being respected. Thanks in advance!
 
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  • #2
yep, all correct. very good.
 

1. What is the formula for calculating the height of a pier above water in projectile motion?

The formula for calculating the height of a pier above water in projectile motion is h = h₀ + v₀sinθt - ½gt², where h is the height, h₀ is the initial height, v₀ is the initial velocity, θ is the angle of launch, t is the time, and g is the acceleration due to gravity.

2. How does the height of the pier affect the trajectory of a projectile?

The height of the pier does not affect the trajectory of a projectile, as long as it is launched at the same angle and with the same initial velocity. The trajectory of a projectile is only affected by the angle of launch and the initial velocity.

3. Can the height of the pier above water be negative in projectile motion?

Yes, the height of the pier above water can be negative in projectile motion. This would indicate that the pier is below the water level. This can occur if the initial height of the projectile is below the water level or if the projectile's trajectory causes it to go below the water level.

4. How does air resistance affect the height of a pier above water in projectile motion?

Air resistance can decrease the height of a pier above water in projectile motion, as it acts as a force in the opposite direction of the projectile's motion. This force can cause the projectile to lose height faster and decrease the overall height of the pier above water.

5. Is the height of the pier above water constant in projectile motion?

No, the height of the pier above water is not constant in projectile motion. It changes as the projectile moves through its trajectory, following the formula h = h₀ + v₀sinθt - ½gt². The height will decrease as the projectile moves downward and increase as it moves upward, eventually reaching a maximum height before falling back down.

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