SOLUTION: A football is kicked at an angle of 37 degrees with a velocity of 20 m/s. Calculate: a.) Maximum height b.) The time of travel before the ball hits the ground c.) The range d.)

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A football is kicked at an angle of 37 degrees with a velocity of 20 m/s. Calculate: a.) Maximum height b.) The time of travel before the ball hits the ground c.) The range d.)      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1044696: A football is kicked at an angle of 37 degrees with a velocity of 20 m/s. Calculate:
a.) Maximum height
b.) The time of travel before the ball hits the ground
c.) The range
d.) The velocity vector at the maximum height
e.) The acceleration vector at the maximum height
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A football is kicked at an angle of 37 degrees with a velocity of 20 m/s.
---
You didn't spec the Earth's gravitational acceleration.
I'll use 10 m/sec/sec
---
Calculate:
a.) Maximum height
Vertical component Vv = 20*sin(37) =~ 12.036 m/sec
Flight time = 12.036*2/10 = 2.407 seconds
---
h(t) = -5t^2 + 12.036t
Max is the vertex @ t = -b/2a = 12.036/10 = 1.2036 seconds
h(1.2036) = 7.243 meters Max height
=============================
b.) The time of travel before the ball hits the ground
2.407 seconds
=====================
c.) The range
Horizontal component = 20*cos(37) =~ 15.973 m/sec
range = 15.973*2.407 = 38.45 meters
=================
d.) The velocity vector at the maximum height
= Horizontal component at angle zero (no vertical speed)
===================
e.) The acceleration vector at the maximum height
= -5 m/sec/sec at all times until impact