1. Revisit the river problem. You are headed west across a river that flows south. The speed of your boat is 15 m/s. The river current is 6 m/s. If the river is 120 m wide (east-west):
a. how long does it take to cross?
b. where do you land?
2. Projectiles at angles. If you were to throw a baseball at 30 m/s at an initial angle of 55 degrees:
a. how long (time) would the ball remain in air until caught (at the same vertical height from which it was released)?
b. how far horizontally would that ball travel during this time?
c. (Tricky part.) How high did the ball rise? Hint: It reaches apogee at the "half-way" point, if the problem is symmetrical (as it is in this case).
*3. For fun. Try to derive the range equation:
R = [ vi^2 / g ] sin (2 theta)
R is the range (also known as the horizontal displacement, dH).
It is useful to know the double angle relation:
sin (2 theta) = 2 sin(theta) cos(theta)
Hint: Set up an equation for dH and plug in something for time.
This is not a trivial problem, so don't get frustrated if you can't get it.
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