Homework Help: calculus

Posted by jessica on Saturday, August 13, 2011 at 7:13pm.

Consider a gun fired from a tower 96ft above the ground. The angle of elevation of the gun is 60 degrees, and its muzzle velocity is 1600 ft/sec (also gravity in this equation is 32 ft/sec^2).
a)When does the bullet hit the ground?
b)Write a parametric equation that models the path of the bullet.
c)What is the range of the gun?
d) find the equation for the bullet based on rectangular coordinates. What type of curve is this?

calculus - Damon, Saturday, August 13, 2011 at 7:42pm
x = u t
y = yi + vi t - 16 t^2
----------------------------
u = 1600 cos 60 = 800 ft/sec the whole time
so
x = u t

vi = 1600 sin 60 = 1386 ft/s
so
y = 96 + 1386 t -16 t^2
so
when is y = 0 ?
0 = 96 + 1386 t - 16 t^2
16 t^2 - 1386 t - 96 = 0
so
t = 86.7 or -.07 (forget negative root)
so hits ground in 86.7 seconds
do u t for range

for part d use t = x/u, u is constant
y = yi + vi (x/u) - 16 x^2/u^2
or
y = c + b x + a x^2 a parabola

Answer this Question

Related Questions

Physics - A hand-pumped water gun is held level at a height of 0.85 m above the ...
Physics - A dart gun is fired while being held horizontally at a height of 0.90 ...
physics - A dart gun is fired while being held horizontally at a height of 0.90 ...
physics - A dart gun is fired while being held horizontally at a height of 1.00 ...
physics - A projectile is fired horizontally from a gun that is 95.0 m above ...
physics - Hello everyone, I need help with this question: A dart gun is fired ...
Phsics - I want to see the calculations.
Physics - The citizens of Paris were terrified during World War I when they were...
phys - A pellet gun is fired straight downward from the edge of a cliff that is ...
physics - A pellet gun is fired straight downward from the edge of a cliff that ...

For Further Reading

First Name:
School Subject:
Answer: