Problem 4-11 - Free fall - Part 11 - (B)

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


Accumulated Solution

\(\mathrm{v = v_0 + at}\)

B coordiantes

\(\mathrm{v_x = v_{0x} + a_xt \\ v_y = v_{0y} + a_yt \\ a_x = 0 \\ a_y = g \\ v_x = v_{0x} \\ v_y = v_{0y} + 9.8t \\ v_x = 24 \cos45 = 17.0\; m/s \\ v_y = 24 \cos45 = 17.0\; m/s \\ v_{0x} = v_{0x} = 17.0 \; m/s} \\ v_{0y} = -2.6 \; m/s \\ v_0 = 17.2 \; m/s\)
 

Correct.

diagram of initial velocity B

\(\theta\) is given by:

(A)   \(\mathrm{tan^{-1} |v_y|/|v_x|}\)

(B)   \(\mathrm{tan^{-1} |v_x|/|v_y|}\)

(C)   \(\mathrm{cos^{-1} |v_y|/|v_x|}\)

(D)   \(\mathrm{sin^{-1} |v_x|/|v_y|}\)