A projectile is fired at an inclination of 45° to the horizontal, with a muzzle velocity of 96 feet per second. The height h of the projectile is given by the following where x is the horizontal distance of the projectile from the firing point.

h(x)= (-32x^2/96^2) + x

How far from the firing point is the height of the projectile a maximum? Give your answer correct to the nearest foot.

Question

A projectile is fired at an inclination of 45° to the horizontal, with a muzzle velocity of 96 feet per second. The height h of the projectile is given by the following where x is the horizontal distance of the projectile from the firing point.

h(x)= (-32x^2/96^2) + x

How far from the firing point is the height of the projectile a maximum? Give your answer correct to the nearest foot.

anonymous · Answer

take the deriv and set equal to zero, this corresponds to v=0 or the peak of it's parabolic motion where h is max.

anonymous · Answer

1-(x/144)=0 solve for x

anonymous · Answer

for max height you plug this value (144) back into the original equation