physics help

Question

On May 20, 1999, Robbie Knieval easily cleared a narrow part of the grand canyon during a world record setting long distance motorcycle jump 69.5m. He left the jump ramp at 10 degrees angle above the horizontal. How fast was he travelling when he left the ramp? Indicate any assumptions you made.

Answer 1

Moxa,

 

I will set this up for you, and you can work the final math.

 

Ignoring air resistance, this is a projectile problem.  The height as a function of time is 

 

y(t) = (-1/2)gt² + (vsinθ)t + y₀

 

g = acceleration of gravity = 9.8 m/s²

 

v = launch velocity = ?

 

θ = 10º

 

y₀ = 0 if launched from ground level

 

Then

 

y(t) = -gt²/2 + (v sinθ)t = t[(-g/2)t + v sinθ]

 

You need to find at what time he is on the ground again.  Set y(t) = 0 and get

 

t = 0 or t = 2v sinθ /g.  The latter is the time he hits the ground.

 

Then the horizontal distance traveled before hitting the ground is

 

x = (v cosθ)t

 

x = 69.5 m (given)

 

Substitute and solve:

 

x = (v cosθ) (2v sinθ /g) = (v²/g)(2 sinθ cos θ) = (v²/g) sin(2θ)

 

Finally,

 

v = [gx / sin(2θ)]^1/2

 

Plug in the given values of g, x, and θ, and you will obtain v in m/s.