Question

Parametric Equations :) 3 parts.

Answer 1

QS: A projectile is fired w initial velocity v knot meters per second at an angle alpha above horizontal and air resistance is negligible, then its position after t seconds is given by parametric equations, \[x=(v_o \cos \alpha )t, y=(v_o \sin \alpha)t - \frac{ 1 }{ 2 }g t^2\] g=9.8m/s^2

a) If a gun is fired with alpha = 30 degrees and v knot = 500m/s, when will the bullet hit the ground? how far from the gun will it hit the ground? what is the max height reached by bullet?
b) use graph to check answers to part (A). Graph path of projectile for several values of alpha to see where it hits.
c) show that the path is parabolic by eliminating parameter.

Answer 2

@ganeshie8

Answer 3

@inkyvoyd

Answer 4

a. [please check]
i) bullet hits the ground at t=51.02
ii) how far bullet is from gun when it hits= approximately 22092.28

Answer 5

a. [please check]
i) bullet hits the ground at t=51.02
ii) how far bullet is from gun when it hits= approximately 22092.28

Answer 6

\[y=(v_0 \sin \alpha)t-\frac{1}{2}g t^2\]\[0=(500\sin 30^0)t-\frac{1}{2}9.8t^2\]solve for t & u will gt ur answer for 1st part

Answer 7

At max height y-direction velocity becomes zero\[v_y=u_y-2gy\]\[0=v_0\sin \alpha -2gh_\text{\max}\]

Answer 8

The x-direction velocity remains constant for whole motion.

so Range=\(v_0 cos \alpha t\)
t=total time for projectile motion