Question

One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching this first snowball, you throw a second snowball at a low angle and time it to arrive at the same time as the first. Assume both snowballs are thrown with the same initial speed 29.3 m/s. The first snowball is thrown at an angle of 63◦ above the horizontal. At what angle should you throw the second snowball to make it hit the same point as the first? The acceleration of gravity is 9.8 m/s 2 . Answer in units of ◦ .

Answer 1

Answer:$27^{\circ}$

Explanation:

Given

Initial velocity of both snowball is 29.3 m/s

first snowball launch angle$=63^{\circ}$

Considering motion of snowball to be projectile

range is given by

$R=\frac{u^2\sin 2\theta }{g}$

$R=\frac{29.3^2\sin 126}{9.8}$

R=70.87 m-----1

If second snowball is thrown at an angle of \phi

$R=\frac{u^2\sin 2\phi }{g}$

$R=\frac{29.3^2\sin 2\phi }{9.8}$------2

$70.87=87.601\sin 2\phi$

$0.809=\sin \phi$

$2\phi can be 53.99^{\circ}$

or $180-2\phi =53.99^{\circ}$

Thus $\phi =26.995 \approx 27^{\circ}$