Explanation Total force acting on the entire system is given as follows: F = N sin θ + μ N cos θ Here, N is the normal force, μ is coefficient of friction and θ is angle of inclination. The above equation can also be written as given below: m a = m g sin θ + μ m g cos θ a = g ( sin θ + μ cos θ ) …… (1) Length of the ramp L = h sin θ …… (2) Speed of the motor is given by using the Newton’s equation of motion as given below: v 2 = u 2 + 2 a s …… (3) Here, s is the length of the ramp. The person sits on the motorcycle now jumps into the pool so it s velocity will be both in x- and y-direction. So, resolve the velocity components as given below: v = v x + v y Here, v x = v cos θ …… (4) v y = v sin θ …… (5) Time for the projectile in air given as below: s y = v y t − 1 2 g t 2 …… (6) Here, s is height of the ramp and g is the acceleration due to gravity. Finally, the distance travel through the air after leaving the end of the ramp is given as follows: x = u t …… (7) Here, u is the initial velocity of the motorcycle. Given: Height of the ramp h = 2.0 m Angle of inclination θ = 20 ο Width of the pool w = 10 m Initial speed of the motorcycle on the ramp u = 11 m/s Coefficient of friction between the tires and dry μ = 0.02 Formula used: a = g ( sin θ + μ cos θ ) L = h sin θ v 2 = u 2 + 2 a s s y = v y t − 1 2 a t Calculation: Substitute, 9.8 m/s 2 for g , angle of inclination θ = 20 ο , u = 11 m/s in equation (1), so the acceleration of motorcycle is given as below: a = 9.8 m/s 2 ( sin ( 20 ο ) + 0.02 cos ( 20 ο ) ) = 3

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

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ISBN: 9780134110684

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Chapter 8, Problem 35EAP

To determine

The distance travel through the air after leaving the end of the ramp

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Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

Ch. 8 - In uniform circular motion, which of the following...Ch. 8 - A car runs out of gas while driving down a hill....Ch. 8 - FIGURE Q8.3 is a bird's-eye view of particles on...Ch. 8 - Tarzan swings through the jungle on a massless...Ch. 8 - FIGURE Q8.5 shows two balls of equal mass moving...Ch. 8 - Ramon and Sally are observing a toy car speed up...Ch. 8 - A jet plane is flying on a level course at...Ch. 8 - A small projectile is launched parallel to the...Ch. 8 - 9. You can swing a ball on a string in a vertical...Ch. 8 - A golfer starts with the club over her head and...

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Kinematics Part 3: Projectile Motion; Author: Professor Dave explains;https://www.youtube.com/watch?v=aY8z2qO44WA;License: Standard YouTube License, CC-BY