Chapter 4.1, Problem 110E

(a)

To determine

Find the angle generated by the skater in each jump with Single axel in radians and degrees.

Answer to Problem 110E

  $3\text{π}\text{rad}\text{;}{540}^0$

Explanation of Solution

Given:

Single axel; 1.5 revolutions ; Double axel; 2.5 revolutions; Triple axel; 3.5 revolutions

Concept Used:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

Calculation:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

In radians: Single axel $=1.5\text{rev}(\frac{2\text{π}\text{rad}}{1\text{rev}})=3\text{π}\text{rad}$

In Degrees: Single axel $=3\text{π}\text{rad}(\frac{{180}^0}{\text{π}\text{rad}})={540}^0$

Thus, the angle generated in single axel is $3\text{π}\text{rad}\text{;}{540}^0$ ;

(b)

To determine

Find the angle generated by the skater in each jump with Double axel in radians and degrees.

Answer to Problem 110E

  $5\text{π}\text{rad}\text{;}{900}^0$

Explanation of Solution

Given:

Single axel; 1.5 revolutions ; Double axel; 2.5 revolutions; Triple axel; 3.5 revolutions

Concept Used:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

Calculation:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

In radians: Double axel $=2.5\text{rev}(\frac{2\text{π}\text{rad}}{1\text{rev}})=5\text{π}\text{rad}$

In Degrees: Double axel $=5\text{π}\text{rad}(\frac{{180}^0}{\text{π}\text{rad}})={900}^0$

Thus, the angle generated in double axel is $5\text{π}\text{rad}\text{;}{900}^0$ .

(c)

To determine

Find the angle generated by the skater in each jump with Triple axel in radians and degrees.

Answer to Problem 110E

  $7\text{π}\text{rad}\text{;}{1260}^0$

Explanation of Solution

Given:

Single axel; 1.5 revolutions ; Double axel; 2.5 revolutions; Triple axel; 3.5 revolutions

Concept Used:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

Calculation:

We know that 1 revolution = $2\text{π}\text{radians}$

  $\text{π}\text{radians}={180}^0$

In radians: Triple axel $=3.5\text{rev}(\frac{2\text{π}\text{rad}}{1\text{rev}})=7\text{π}\text{rad}$

In Degrees: Triple axel $=7\text{π}\text{rad}(\frac{{180}^0}{\text{π}\text{rad}})={1260}^0$

Thus, the angle generated in triple axel is $7\text{π}\text{rad}\text{;}{1260}^0$