In 1999, Robbie Knievel was the first to jump the Grand...

Name: Problem 57, Chapter 4: University Physics Volume 1
Uploaded: 2021-05-29T23:02:38-08:00
Duration: 1 min 22 s
Channel: Suzanne W.
Description: In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?

In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?

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Key Concepts

Projectile Motion

Projectile motion describes the trajectory of an object launched into the air, which then moves under the influence of gravity. It involves decomposing the initial velocity into horizontal and vertical components, with the horizontal motion being uniform (constant velocity if air resistance is neglected) and the vertical motion being accelerated under the force of gravity.

Range Equation

The range equation provides a formula to calculate the horizontal distance traveled by a projectile, assuming it lands at the same elevation from which it was launched. This equation is given by R = (v² sin(2?))/g, where v is the initial speed, ? is the launch angle, and g is the acceleration due to gravity. This relationship is essential in determining the angle required to achieve a specific horizontal distance.

Trigonometric Relationships in Kinematics

Trigonometric relationships play a critical role in projectile motion by linking the components of the initial velocity with the launch angle. The sine function specifically appears in the range equation, where sin(2?) relates the double angle of the launch with the product of the gravitational acceleration and the required distance. These relationships allow for the calculation of unknown parameters, such as the launch angle, given other known quantities.

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