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 11.1 m/s. the first
snowball is thrown at an angle of 67◦
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 ◦
.
007 (part 2 of 2) 10.0 points
how many seconds after the first snowball
should you throw the second so that they
arrive on target at the same time?
answer in units of s.

Answers:

a)

b)

Explanation:

This situation is a good example of the projectile motion or parabolic motion, in which the travel of the snowball has two components: x-component and y-component. Being their main equations as follows for both snowballs:

x-component:

  (1)

Where:

is the initial speed  of snowball 1 (and snowball 2, as well)

is the angle for snowball 1

is the time since the snowball 1 is thrown until it hits the opponent

y-component:

  (2)

Where:

 is the initial height of the snowball 1 (assuming that both people are only on the x axis of the frame of reference, therefore the value of the position in the y-component is zero.)

 is the final height of the  snowball 1

 is the acceleration due gravity (always directed downwards)

x-component:

  (3)

Where:

is the angle for snowball 2

is the time since the snowball 2 is thrown until it hits the opponent

y-component:

  (4)

Having this clear, let's begin with the answers:

Firstly, we have to isolate from (2):

  (5)

  (6)

Substituting (6) in (1):

  (7)

Rewritting (7) and knowing :

  (8)

  (9)

  (10)  This is the point at which snowball 1 hits and snowball 2 should hit, too.

With this in mind, we have to isolate from (4) and substitute it on (3):

  (11)

  (12)

Rewritting (12):

  (13)

Finding :

  (14)

 (15) This is the second angle at which snowball 2 must be thrown. Note this angle is lower than the first angle .

Now we will find the value of and from (6) and (11), respectively:

  (16)

  (17)

  (18)

  (19)

Since snowball 1 was thrown before snowball 2, we have:

  (20)

Finding the time difference between both:

  (21)

Finally:

you can cut your hand off if your not