Question

A fisherman casts his bait toward the river at an angle of 25° above the horizontal. The bait and hook reach a maximum height of What was the initial velocity with which the bait was cast? Assume that the fishing line exerts no appreciable drag force on the bait and hook.

Answer 1

What was the maximum height?

Answer 2

is 3.2 m

Answer 3

Since the initial velocity is at an angle, you can decompose it into horizontal (vcosθ) and vertical (vsinθ) components. Let's focus on the vertical component because we're talking about height, which is a vertical thing.

Keep in mind that at the maximum height, the vertical velocity is 0 m/s. Using the initial velocity, vsinθ, and g as the acceleration, we have the following equation from a=v/t:

\[g={v \sin \theta \over t} \implies t={v \sin \theta \over g}\]
Unfortunately, this equation uses t, which we don't know. However, if we can find another equation that uses v and t, we'll have a system of equations that we can solve. Luckily we can find this second equation using the height given and the equation d=vt+½at^2:

\[h=v \sin \theta t-{1 \over 2}at^2\]
Now you should be able to combine these two equations and solve for v! What do you get?