Question

8) A football is kicked off the flat ground at 26.0 m/sat an angle of 30∘ relative to the ground.

a) Determine the total time it is in the air.

b) Find the angle of its velocity with respect to the ground after it has been in the air for one-fourth of this time

c) Repeat for one-half of the total time.

d) Repeat for three-fourths of the total time.

e) For each of these times, determine its speed.

Answer 1

a) time of flight t = 2v0sin(theta)/g

t = 2*26*sin30/9.8 = 2.65 sec

b) t' = t/4 = 0.6625 sec

vx = v0cos30 = 22.52 m/s

vy = v0sin30-gt' = 6.51 m/s

v = sqrt(vx^2+vy^2) = 23.4 m/s

theta = tan^-1(6.51/22.52) = 16.1 degrees

c) one half time vy = 0

vx = 22.52 m/s

theta = zero

d) three-fourth of time

t' = 3t/4 = 1.99 sec

vx = 22.52 m/s

vy = 26sin30-9.8*1.99 = -6.5 m/s

v = sqrt(22.52^2+6.5^2) = 23.44 m/s

theta = tan^-1(-6.5/22.52) = 16.1 degrees below the axis

e) if t' = t/4

v = 23.4 m/s

if t' = t/2

v = 22.52 m/s

if t' = 3t/4

v = 23.44 m/s