A motorcycle rider plans to make a jump off a ramp. If he leaves the ramp with a speed of 38.0m/s and has a speed of 36.3m/s at the top of his trajectory, determine his max height above the end of the ramp. Ignore friction and air resistance. i got 6.45m but i really don't know if I'm doing the question right...

u = constant horizontal velocity = 36.3

so
36.3 = 38 cos theta
so
theta = 17.2 degrees above horizontal

Vi = initial vertical velocity
= 38 sin theta = 38 sin 17.2 = 11.2 m/s

v = Vi - 9.81 t
at top v = 0
so
t = 11.2/9.81 = 1.15 seconds to top

h = Vi t - 4.9 t^2
= 11.2(1.15) - 4.9 (1.15)^2
= 12.8 - 6.4
= 6.4 meters
I think you did it right

Thank you!

To determine the maximum height above the end of the ramp, you can use the principles of projectile motion. Since there is no air resistance or friction, we can assume that the only forces acting on the motorcycle rider are gravity and the normal force.

Here's how you can approach this problem:

Step 1: Determine the initial vertical velocity (v₀y) of the rider when leaving the ramp. This can be found using the equation:

v = v₀ + at

where:
- v = final velocity (36.3 m/s)
- v₀ = initial velocity (38.0 m/s)
- a = acceleration (due to gravity, approximately -9.8 m/s²)
- t = time

Rearranging the equation, we have:

t = (v - v₀) / a

Substituting the given values:

t = (36.3 - 38.0) / -9.8
t ≈ 0.173 seconds

Step 2: Calculate the maximum height (h) above the end of the ramp using the equation:

h = v₀y * t + (1/2) * a * t²

Since the rider starts at the top of the trajectory with zero vertical velocity, v₀y = 0. Therefore, the equation simplifies to:

h = (1/2) * a * t²

Substituting the given values:

h = (1/2) * (-9.8) * (0.173)²
h ≈ -0.057 meters

Here's where you might have made a mistake. The negative sign for height indicates that the rider falls below the end of the ramp, rather than climbing above it. Therefore, the calculated value of -0.057 meters (or approximately -5.7 cm) is incorrect.

Based on the calculations, it seems there may be an error in the values or the approach used. Please double-check the given information and equations to ensure accuracy.