Problem 4-11 - Free fall - Part 7 - (A)

A ball is thrown from a balloon with an initial unknown velocity. The ball accelerates at \(9.80\;m/s^2\) downward for \(2.00\; s\), at which time its instantaneous velocity is \(24.0\; m/s\) at an angle of \(45.0^\circ\) below the horizontal. Determine the magnitude and direction of the initial velocity.

Accumulated Solution

\(v = v_0 + at\)

\(v_x = v_{0x} + a_xt \\ v_y = v_{0y} + a_yt \\ a_x = 0 \\ a_y = g \\ v_x = v_{0x} \\ v_y = v_{0y} + 9.8t \\ v_x = 24 \cos45 = 17.0\; m/s \\ v_y = 24 \cos45 = 17.0\; m/s\)

Correct.

The components of \(v\) are:

\(v_x = 24 \cos45 = 17.0\; m/s \\ v_y = 24 \cos45 = 17.0\; m/s\)

What is the \(x\) component of \(v_0\)?

(A)   \(17.0 + 9.8(2) = 36.6\; m/s\)

(B)   \(17.0\; m/s\)

(C)   \(17.0 - 9.8(2) = 2.6 \;m/s\)