Chapter 10.6, Problem 58PE

(a)

To determine

To calculat e: The parametric equations to define the path of the motorcycle as a function of the time $t$ (in sec) after leaving the ramp.

Given, a daredevil on a motorcycle travels approximately $88\text{ ft/sec}$ $\left(60\text{mph}\right)$ at an angle of $30°$ when the motorcycle leaves the ramp at the edge of the canyon.

(b)

To determine

Whether the motorcycle hit the bird if a bird is at a position $\left(90,26\right)$ at a time $1.2\text{ sec}$ after the motorcycle leaves the ramp. Given, the daredevil on the motorcycle travels approximately $88\text{ft/sec}$ $\left(60\text{mph}\right)$ at an angle of $30°$ when the motorcycle leaves the ramp at the edge of the canyon.

(c)

To determine

To calculat e: The horizontal distance travelled across the canyon from the take-off point to the point of landing of the motorcycle of the daredevil who travels approximately $88\text{ ft/sec}$ $\left(60\text{mph}\right)$ at an angle of $30°$ when the motorcycle leaves the ramp at the edge of the canyon.

(d)

To determine

The coordinates (to the nearest foot) of the motorcycle at its maximum height if a daredevil travels approximately $88\text{ ft/sec}$ $\left(60\text{mph}\right)$ at an angle of $30°$ when the motorcycle leaves the ramp at the edge of the canyon.

(e)

To determine

The equation representing the path in rectangular coordinates. Given, a daredevil on his motorcycle travels approximately $88\text{ ft/sec}$ $\left(60\text{mph}\right)$ at an angle of $30°$ when the motorcycle leaves the ramp at the edge of the canyon.