cq_1_082

PHY 121

Your 'cq_1_08.2' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.

** **

A ball is tossed upward at 15 meters / second from a height of 12 meters above the ground. Assume a uniform downward acceleration of 10 m/s^2 (an approximation within 2% of the 9.8 m/s^2 acceleration of gravity).

• How high does it rise and how long does it take to get to its highest point?

• How fast is it then going when it hits the ground, and how long after the initial toss does it first strike the ground?

• At what clock time(s) will the speed of the ball be 5 meters / second?

• At what clock time(s) will the ball be 20 meters above the ground?

• How high will it be at the end of the sixth second?

answer/question/discussion: ->->->->->->->->->->->-> :

Question 1a. y = (v^2 – v0^2 / 2 a) + 12 m

y = ((0 – (15 m/s)^2) / 2 ( -10 m/s^2)) +12 m

y = ((0 – 225 m/s) / -20 m/s^2) + 12 m

y = (-225 m/s / -20 m/s^2) + 12 m

y = 11.25 m + 12 m

y = 23.25 m is how high the ball goes in the air.

Question 1b. y = -( v0 / a)

y = - (15 m/s / (-10 m/s^2))

y = -(-1.5 s)

y = 1.5 s is how long it takes it to reach it’s highest point.

Question 2a. y = v0t + ½ at^2

0 = (15 m/s)t + ½ (-10 m/s^2)t^2

0 = (15 m/s – 5 m/s^2t)t

t = 15 m/s / 5 m/s^2

t = 3 s is how long it take for the ball to hit the ground.

Question 2b. v = v0 + at

v = 15 m/s – (10 m/s^2) (3 s)

v = 15 m/s – 30 m/s

v = -15 m/s is the velocity of the ball when it hits the ground.

Question 3. v = v0 + at

v = 15 m/s – (10 m/s^2)( 5 s) = -35 m/s

Question 4. y = y0 + v0t + ½ at^2

20 m = 0 + (15 m/s)t + ½ (-10 m/s^2)t^2

(-5 m/s^2)t^2 – (15 m/s)t + (20 m) = 0

t = 15 m/s +-‘sqrt((15 m/s)^2 – 4(-5 m/s^2)(20 m)) / 2(5 m/s^2)

t = 15 m/s +-‘sqrt(225 m/s – (-400 m/s)) / 10 m/s^2

t = 15 m/s +-‘sqrt(625) / 10 m/s^2

t = (15 m/s +- 25) / 10 m/s^2

t = (15 m/s + 25) / 10 m/s^2 = 4 s

t = (15 m/s – 25) / 10 m/s^2 = -1 s

Question 5. If it hits the ground after 3 s it would be at 0 after 6 seconds.

** **

30 minutes

** **

&#Good responses. Let me know if you have questions. &#