How do I correctly solve this trigonometry problem?

Question

I was assigned this question for homework and got it wrong. How do I answer it?

A projectile is fired with initial velocity of v(subscript 0) feet per second. The projectile can be pictures as being fired from the origin into the first quadrant, making an angle theta with the positive x-axis. If there is no air resistance, then at t seconds the coordinates of the projectile (in feet) are x=v(subscript 0)tcos(theta) and y= -16t(squared)+v(subscript 0)tsin(theta). Suppose a projective leaves the gun at 100 ft/sec and theta=60 degrees.
A. What are the coordinates of the projectile at time t=4 seconds?
B. For how many seconds is the projectile in the air?
C. How far from the gun does the projectile land?
d. What is the maximu height attained by the projectile:
e. Find an expression in terms of v(subscript 0) and theta for the time in the air.
f. Find an expression in terms of v (subscript 0) and theta for the distance from the gun.

g. Find an expression in terms of v(subscript 0) and theta for the maximum height.
h. Show that y= -(16sec(squared)theta)/(v(squared)(subscript 0))x(squared)+xtan(theta).

Answer 1

X=vtcos(theta)
y=-16t^2 + Vsub0t*sin(theta)
A: Plug in 4 for t, and 60 for theta, 100ft/s for velocity. then you get the Y value. For the X value, which is distance can be solved through Tangent function. Tan(Theta)= Y/x. X= Y/Tan(theta)
B: Plug in for Y=0 and solve
C: When you get the time from (B) plug it in the first equation, x=vt...
D: Max height, got a graphing calculator? if not -b/2a last i recalled.
E: not sure
F: not sure

Answer 2

Hi. Whew, that would be a lot of work! You have the formula, just plug in the numbers! OK, just read that you got it wrong, so you tried. Funny that the units are feet but it makes no difference. How about we do the first.

x=v0*t(cos(theta)) so substitute ; x=100*4(cos 60) and
y= -16t^2+v0*t(sin(theta)) ; y=-16*4^2 + 100*4(sin 60)

Now just use your calculator. Hope this helps!

Answer 3

If I were you - I'd go sick!