Answer:
22.5°
Explanation:
<u>Short answer</u>: The trajectories will hit the same target when the projectile is launched at complementary angles. The second angle is 90° -67.5° = 22.5°.
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<u>Longer answer</u>: The horizontal speed of the snowball launched at angle α with speed s is ...
vh = s·cos(α)
Then the horizontal distance at time t is ...
x = vh·t
and the time taken to get to some distance x is ...
t = x/vh = x/(s·cos(α))
The equation for the vertical motion of the projectile is ...
y = -4.9t² +s·sin(α)·t
Substituting the above expression for t, we have y in terms of x:
y = -4.9x²/(s·cos(α))² +(s·sin(α)·x)/(s·cos(α))
Factoring gives ...
y = (x/(cos(α))(-4.9x/(s²·cos(α)) +sin(α))
The height y will be zero at x=0 and at ...
0 = -4.9x/(s²·cos(α)) +sin(α)
x = s²·sin(α)·cos(α)/4.9 = (s²/9.8)sin(2α)
So, for some alternate angle β, we want ...
sin(2α) = sin(2β)
We know this will be the case for ...
2β = 180° -2α
β = 90° -α
The second snowball should be thrown at an angle of 90°-67.5° = 22.5° to make it hit the same point as the first.
