Amotorcycle daredevil wants to ride up a 50.0-m ramp set at a 30 degree incline to the ground. it will launch him in the air and he wants to come down so he just misses the last of a number of 1.00m diameter barrels. if the speed at the instant when he leaves the ramp is 60.0 m/s, how many barrels can be used?

i tried to make a diagram and i looked up the answer so i know its approx 355 but i dont know how to solve it.

356

Explanation:

First, find the time it takes for the daredevil to land.

Given (in the y direction):

Δy = -50.0 sin 30° m = -25.0 m

v₀ = 60.0 sin 30° m/s = 30.0 m/s

a = -9.8 m/s²

Find: t

Δy = v₀ t + ½ at²

(-25.0 m) = (30.0 m/s) t + ½ (-9.8 m/s²) t²

4.9t² − 30t − 25 = 0

Solve with quadratic formula:

t = -0.743 s or 6.87 s

t must be positive, so t = 6.87 s.

Next, find the horizontal distance traveled in that time.

Given (in the x direction):

v₀ = 60.0 cos 30° m/s = 52.0 m/s

a = 0 m/s²

t = 6.87 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (52.0 m/s) (6.87 s) + ½ (0 m/s²) (6.87 s)²

Δx = 356.7 m

Rounding down to the nearest meter, Δx = 356 m.

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.

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