If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)?

Problem 2

A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (assume a uniform acceleration).

**Problem 3**

A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.)

**Problem 10**

**With what speed in miles/hr (1 m/s = 2.23 mi/hr) must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance.**

Given:

a = -9.8 m/s^2

vf = 0 m/s

d = 1.29 m

Find:

vi = ?

t = ?

Problem 1

Solution:

for vi,

vf^2 = vi^2 +2ad

(0 m/s)^2 = vi^2 + 2(-9.8m/s^2)(1.29m)

vi^2 = 25.28 m^2/s^2

vi = 5.03 m/s

for t,

vf = vi + at

0 m/s = 5.03 m/s + (-9.8m/s^2)t

t = (5.03m/s)/(-9.8m/s^2)

t = 0.513 s

Given:

vi = 0 m/s

vf = 521 m/s

d = 0.840 m

Find:

a = ?

Problem 2

Solution:

for a,

vf^2 = vi^2 + 2ad

(521 m/s)^2 = (0 m/s)^2 + 2a(0.840 m)

a = (271441 m^2/s^2)/(1.68 m)

a = 1.62 x10^5 m/s^2

**Problem 4**

**Problem 5**

Problem 6

Problem 7

**Problem 8**

**Problem 9**

The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below.

A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.)

A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well.

It was once recorded that a Jaguar left skid marks that were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it began to skid.

A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed.

A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster.

Problem 4

Solution:

d = vit + 0.5(at^2)

-370 m = (0 m/s )t + 0.5(-9.8m/s^2)t^2

t^2 = (-370 m)/(-4.9 m/s^2

t^2 = 75.5 s^2

t = 8.69 s

Problem 3

Solution:

Use first, vf = vi + at

0 m/s = vi + (-9.8 m/s^2)(3.13 s)

vi = 30.6 m/s

Now use, vf^2 = vi^2 + 2ad

(0 m/s)^2 = (30.6 m/s)^2 + 2(-9.8m/s^2)d

d = (-938 m/s )/(-19.6 m/s^2)

d = 47.9 m

Given:

vi = 0 m/s

d = -370 m

a = -9.8 m/s^2

Find:

t = ?

Problem 5

Solution:

vf^2 = vi^2 +2ad

(0 m/s^2) = (367 m/s)^2 + 2a(0.0621 m)

a = (-134689 m^2/s^2)/(0.1242 m)

a = -1.08 x 10^6 m/s^2

Given:

vi = 367 m/s

vf = 0 m/s

d = 0.0621 m

Find:

a = ?

Problem 6

Solution:

d = vit + 0.5a(t^2)

d = (0 m/s)(3.41 s) + 0.5(-9.8 m/s^2)(3.41 s)^2

d = 0 + 0.5(9.8 m/s^2)(11.63 s^2)

d =-57.0 m

Given:

a = -9.8 m/s^2

t = 3.41 s

vi = 0 m/s

Find:

d = ?

Given:

a = -3.90 m/s^2

vf = 0 m/s

d = 290 m

Find:

vi = ?

Problem 7

Solution:

vf^2 = vi^2 +2ad

(0 m/s)^2 = vi^2 + 2(-3.90m/s^2)(290 m)

2262 m^2/s^2 = vi^2

vi = 47.6 m/s

Given:

vi = 0 m/s

vf = 88.3 m/s

d = 1365 m

Find:

a = ?

t = ?

Problem 8

Solution:

for a, vf^22 = vi^2 +2ad

(88.3 m/s)^2 = (0 m/s)^2 + 2a(1365 m)

(2730 m)a = 7797 m^2/s^2

a = (7797 m^2/s^2)/(2730 m)

a = 2.86 m/s^2

for, t vf = vi + at

88.3 m/s^2 = 0 m/s + (2.86 m/s^2)t

t = (88.3 m/s)/(2.86m/s^2)

t = 30.8 s

Given:

vi = 0 m/s

vf = 112 m/s

d = 398 m

Find:

a = ?

Problem 9

Solution:

vf^2 = vi^2 +2ad

(112 m/s)^2 = (0 m/s)^2 + 2a(398 m)

12544 m^2/s^2= a(796 m)

a = (12544 m^2/s^2)/(796 m)

a = 15.8 m/s^2

**Given:**

a = -9.8 m/s^2

vf = 0 m/s

d = 91.5 m

a = -9.8 m/s^2

vf = 0 m/s

d = 91.5 m

**Find:**

vi = ?

t = ?

vi = ?

t = ?

Problem 10

Solution:

First, Find speed, vf^2 = vi^2 +2ad

(0m/s)^2 = vi^2 + 2(-9.8 m/s^2)(91.5 m)

vi^2 = 1793 m^2/s^2

vi = 42.3 m/s

Now, convert from m/s to mi/hr

vi = 42.3 m/s(2.23 mi/hr)/(1 m/s)

vi =94.4 mi/hr