Chapter 3.3, Problem 45PP

a.

To determine

The velocity and acceleration at the top.

Answer to Problem 45PP

At the top velocity $v\text{= 0 m/s}$ and acceleration $a\text{=9}{\text{.8 m/s}}^{-2}$ .

Explanation of Solution

Given:

Acceleration $a\text{=9}{\text{.8 m/s}}^{-2}$

Formula Used:

  $v=u+at$

  $v^2=u^2+2as$

v is the final velocity

u is the initial velocity

t is the time

s is the distance

a is the acceleration.

Calculation:

At the top of the trajectory the coin is at rest, hence the velocity is $v\text{= 0 m/s}$ .

As the coin is flipped it is constantly under the influence of the gravity, hence at the top of the projectile acceleration $a\text{=9}{\text{.8 m/s}}^{-2}$ .

Conclusion:

At the top velocity $v\text{= 0 m/s}$ and acceleration $a\text{=9}{\text{.8 m/s}}^{-2}$ .

b.

To determine

The initial velocity.

Answer to Problem 45PP

  $u=2.21\text{ m/s}$

Explanation of Solution

Given:

Final velocity $v=0\text{ m/s}$

Distance travelled $s=0.25\text{ m}$

Formula Used:

  $v^2=u^2+2as$

v is the final velocity

u is the initial velocity

t is the time

s is the distance

a is the acceleration.

Calculation:

  $v^2=u^2+2as$

Substituting the values

  $0=u^2+2\left(\text{-9}{\text{.8 m/s}}^{-2}\right)(0.25\text{ m})$

  $u^2=2\left(\text{9}{\text{.8 m/s}}^{-2}\right)(0.25\text{ m})$

  $u=2.21\text{ m/s}$

Conclusion:

The initial velocity of the coin $u=2.21\text{ m/s}$ .

c.

To determine

The total time taken in the flip.

Answer to Problem 45PP

The total time taken in the flip is $0.44\text{ s}$ .

Explanation of Solution

Given:

Final velocity $v=0\text{ m/s}$

The initial velocity of the coin $u=2.21\text{ m/s}$

Distance travelled $s=0.25\text{ m}$

Formula Used:

  $v=u+at$

v is the final velocity

u is the initial velocity

t is the time

a is the acceleration.

Calculation:

  $v=u+at$

Calculation the time taken to reach the highest point.

Substituting the values

  $0=2.21\text{m/s+}\left(\text{-9}{\text{.8 m/s}}^{-2}\right)t$

  $t=\frac{2.21\text{m/s}}{\left(\text{9}{\text{.8 m/s}}^{-2}\right)}$

  $t=0.22\text{ s}$

The total time is twice the time taken to reach the highest point.

Total time is $T=2t=0.44\text{ s}$

Conclusion:

The total time taken in the flip is $0.44\text{ s}$ .