Classic physics problem - There is a squirrel sitting in a tree at height H. On
ID: 1528811 • Letter: C
Question
Classic physics problem - There is a squirrel sitting in a tree at height H. On the ground, some distance D away from the tree is a hunter with a rifle(muzzle velocity of V_0). At the moment the gun is fired, the squirrel lets go of the branch he is holding onto and free falls straight down. What angle does the hunter aim to hit the squirrel? Make a prediction. Should the hunter aim above, at or below the squirrel? Write an algebraic expression for height of the squirrel. Write an algebraic the height of the bullet. Set the two expressions for height equal and solve for sin (theta). What time is it when the bullet meets the squirrel (at distance D)? Take your expression for time and substitute it into your expression for sin(theta) which should have time in it... do you see tan(theta) in there?Explanation / Answer
3)
(a)
The hunter should aim below the sqirrel !!
(b)
Height of the squirrel with time t,
s = u*t + 1/2*g*t^2
s = 0 + 1/2*g*t^2
Height of the squirrel above the ground, = H - 1/2*g*t^2
(c)
Verttical velocity of bullet, = vo*sin()
s = vo*t - 1/2*g*t^2
s = vo*sin() * t - 1/2*g*t^2
Height of the bullet, = vo*sin() * t - 1/2*g*t^2
(d)
H - 1/2*g*t^2 = vo*sin() * t - 1/2*g*t^2
H = vo*sin() * t
sin() = H/(vo*t)
(e)
Horizontal velocity of bullet, = vo*cos()
Horizontal distance travelled by bullet = D
Time taken, t = D/( vo*cos())
(f)
sin() = H/(vo*t)
sin() * t = H/vo
sin() * D / (vo * cos()) = H/vo
tan() * D/vo = H/vo
tan() = H/D