SOLUTION: Charlie Brown punts a football, which leaves his foot at a height of 3 ft above the ground and with an initial upward velocity of 70 ft/sec. The vertical velocity of the football t

Algebra ->  Equations -> SOLUTION: Charlie Brown punts a football, which leaves his foot at a height of 3 ft above the ground and with an initial upward velocity of 70 ft/sec. The vertical velocity of the football t      Log On


   

Question 1116037: Charlie Brown punts a football, which leaves his foot at a height of 3 ft above the ground and with an initial upward velocity of 70 ft/sec. The vertical velocity of the football t seconds after it is punted is given by v(t)=-32t+70, where v is in feet per second.(Note that velocity is the derivative of height.)
Snoopy catches the football 5 ft above the ground. What is the vertical velocity of the ball immediately before it is caught? Round final answer to four decimal places, but do not round in intermediate steps.
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are two ways to solve this problem. 

One way is Algebra. You need to use this equation for the height  h(t) = -16*t^2 +70t + 3;  find the time moment when h(t) = 5 ft  
(on the way up or down - it does not matter !); then calculate the velocity using the given formula for that value of "t".


This way is long and boring.


Another way is to use the energy conservation law of Physics,  which says

%28mV%5E2%29%2F2 = %28mv%5E2%29%2F2 - mg%2Adelta_H,    (1)


where v = 70 ft/s is the given velocity;  V  is the velocity under the question at the height of 5 ft; 

delta_H = 2 ft is the difference of levels;  m is the mass of the ball and g = 32 ft/s^2 is the gravity acceleration.


Cancel "m" in both sides of the equation (1) to get

%28V%5E2%29%2F2 = %28v%5E2%29%2F2 - g%2Adelta_H,    (1)


substitute the values

V%5E2%2F2 = 70%5E2%2F2 - 2%2A32.


and complete the calculations on your own.  You goal is to find the capital V !