Question

A ball is thrown straight upward from a height of 1.0 m with a velocity of 2.0 m/s.

(a) Write an equation to describe the ball’s height as a function of time.

(b) What is the maximum height the ball reaches?

(c) After how many seconds does the ball hit the ground? 3.

On a drive from Philadelphia to Newark, you drive 2/3 of the distance at 80 kilometers per hour. You then get stuck in a construction zone and have to drive at 35 kilometers per hour for the remaining 1/3 of the distance.

(a) Sketch x(t), assuming that all motion is in the +x direction. Indicate how average velocity can be found on your sketch.

(b) What is your average velocity in km/hour (including direction) for the trip? (You do not need to know the exact distance from Philadelphia to Newark to answer this question.)

Answer 1

along vertical

initial velocity voy = 2 m/s

initial height yo = 1 m

acceleration ay = -g - 9.8 m/s^2

from equation of motion

y - yo = voy*t + (1/2)*ay*t^2

---------------------

(b)

at maimum height final velocity vy = 0

vy^2 - voy^2 = 2*ay*(y-y0)

0 - 2^2 = -2*9.8*(ymax - 1)

maimum height yma = 1.2 m

==============

(c)

after hitting ground final position y = 0

y - yo = voy*t + (1/2)*ay*t^2

0 - 1 = 2*t - (1/2)*9.8*t^2

t = 0.7 seconds

====================================

(b)

total displacement = S

total time T = (2/3)*S/v1 + (1/3)*S/v2 = 2S/(3v1) + S/(3V2) = S*(2V2 + V1)/(3*V1*V2)

average velocity V = S/T

average velocity = 3*V1*V2/(2V2 + V1) = (3*80*35)/((2*35)+80)

average velocity = 56 kilometer per hour