Problema Solution
So carlos and maria are finally done driving. They got to their final destination. With all of their practice driving, they get an idea. Try to jump their car over a river that is 225 feet wide. So they get started building a ramp. the ramp is 26 feet high. they figure that if they drive 75 miles per hour then they will make it. The equation for their jump is d=-16tsquare + 110t+26. how high off the ground will they get and how far will they jump? do they make it across or should they study more math?
Answer provided by our tutors
To find the maximum height of the jump, take the derivative of the jump equation with respect to t and set it to zero:
-32t + 110 = 0
32t = 100
t = 3.125
Then plug t into the original equation: -16(3.125)^2 + 110(3.125) +26 = 213.5
They will get a maximum height of 213.5 feet off of the ground.
To find out whether they will make it across the river, set the original equation equal to zero and solve:
-16t^2 + 110t + 26 = 0
Using quadratic formula: (-110 +/- sqrt(110^2 - 4(-16)(26)))/2(-16)
t = 7.10 seconds
and
t = -0.23 seconds
Choose t = 7.10 seconds and figure out how far the 75mph-travelling car would make it in that amount of time:
75mph is 110 feet per second.
So 110fps * 7.10s = 781 feet.
They make it across.