A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; #y=-16t^2+32t#, At what two times will the ball be at a height of 6ft.?

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Answer 1 · 2017-07-15T22:38:23

time #= 0.2094, 1.7906 \ \ \ ("unit")\ \ (4dp)#

We have:

# x = 50t #
# y=-16t^2+32t #

On the assumption that #t# represents time, and #x# and #y# are the horizontal and vertical displacements respectively in feet then we note that:

Horizontal displacement is linear
Vertical displacement is parabolic

So for the vertical displacement to be #6# feet we require:

# -16t^2+32t = 6 #
# :. 16t^2 -32t+ 6 = 0#

And using the quadratic formula we form two solutions:

# t = 1+-1/2sqrt(5/2) #
# \ \ = 0.2094, 1.7906 \ \ (4dp)#