When a mortar shell is ﬁred with an initial
velocity of v0 ft/sec at an angle α above the
horizontal, then its position after t seconds is
given by the parametric equations
x = (v0 cos α)t , y = (v0 sin α)t − 16t^2.
If the mortar shell hits the ground 2500 feet
from the mortar when α = 75degress, determine v0
*answer choices*
1. v0 = 360 ft/sec
2. v0 = 370 ft/sec
3. v0 = 380 ft/sec
4. v0 = 390 ft/sec
5. v0 = 400 ft/sec

Question

When a mortar shell is ﬁred with an initial
velocity of v0 ft/sec at an angle α above the
horizontal, then its position after t seconds is
given by the parametric equations
x = (v0 cos α)t , y = (v0 sin α)t − 16t^2.
If the mortar shell hits the ground 2500 feet
from the mortar when α = 75degress, determine v0
*answer choices*
1. v0 = 360 ft/sec
2. v0 = 370 ft/sec
3. v0 = 380 ft/sec
4. v0 = 390 ft/sec
5. v0 = 400 ft/sec

dumbcow · Answer

from x equation:
$$t = \frac{x}{v*\cos \theta} = \frac{2500}{v*\cos 75}$$
substitute this into y equation
$$0 = v*\sin 75(\frac{2500}{v*\cos 75}) -16(\frac{2500}{v*\cos 75})^{2}$$
solve for v
v = 400