Answer:
The motorcycle daredevil does not sail across the 10-m wide pool filled with hungry crocodiles
Step-by-step explanation:
The given parameters are;
The height of the ramp = 2.0 m-high
The angle of elevation of the ramp, θ = 20°
The width of the pool = 10 m
The speed with which he is going when the engine fails = 10.4 m/s
The rolling friction between the rubber tires, μ = 0.02
μ·g·cos(θ) = (1/2)·(a)
a = (μ·g·cos(θ))/(1/2)
Where;
a = The acceleration down the plane
∴ a = 0.02 × 9.81 × cos(20°)/(1/2) ≈ 0.369
The length of the ramp, l = 2.0 m/(sin(20°)) ≈ 5.8476088 m
The velocity at the end of the ramp, v² = u² - 2·a·l
∴ v² = 10.4² - 2×(0.369 + 9.81 × sin(20°))×5.8476088 ≈ 64.60446471
v ≈ √(64.60446471) ≈ 8.04
∴ The velocity at the top of the ramp, v ≈ 8.04 m/s
The time it takes the motorcycle to reach ground level from the top of the ramp, t, is given as follows;
h = h₀ + u·t + (1/2)·a·t²
h₀ = 2, u = 8.04×sin(20°), a = -9.81
When h = 0 (ground level), we have;
∴ h = 2+ 8.04×sin(20°)·t - (1/2)×9.81×t²
0 ≈ 2.75·t - 4.905·t² + 2
2.75·t - 4.905·t² + 2 = 0
By using a graphing calculator, we have, t = 0.978 or t = -0.42
At ground level, the time of flight, t ≈ 0.978 s
The horizontal distance the motorcycle travels, before landing, x = u × cos(θ) × t
∴ x = 8.04×cos(20 Degrees) × 0.978 = 7.3889
The horizontal distance the motorcycle travels, before landing, x ≈ 7.3889 m
Therefore, given that the horizontal distance the motorcycle travels in the air 7.3889 m < 10 m, therefore the motorcycle daredevil does not sail across the 10-m wide pool filled with hungry crocodiles