Question

With time running out in a game, Rachel runs towards the basket at a speed of 2.5 meters per second and from half-court, launches a shot at a speed of 8 meters per second at an angle of36° to the horizontal.
a. Write the component form of the vectors representing Rachel’s velocity and the path of the ball.b. What is the resultant speed and direction of the shot?

Answer 1

Answer:

Rachel(2.5,0)

ball(6.5,4.7)

b.R=10.15m/s, 27.57deg

Explanation:

The reference angle of Rachel is 0$0^{0} while the ball is at 36^{0}$

resolving rachel's speed to the horizontal, we have

Ux=2.5cos0

Ux=2.5m/s

resolving rachel's speed to the vertical we have,

Uy=2.5sin0

Uy=0

for the ball

resolving the speed to its horizontal component

Ux=8cos36

Ux=6.5m/s

Uy=8sin36

Uy=4.7m/s

Rachel(2.5,0)

ball(6.5,4.7)

To get the resultant of their speed

Add the horizontal speed of rachel to that of the ball to get the total horizontal speed

Add the vertical speed of rachel and the ball to get the total vertical speed component

TUx=2.5+6.5=9M/S

TUy=0+4.7=4.7m/s

R=$\sqrt{(TUx^2+TUy^2}$

R=$\sqrt{(9^2+4.7^2}$

R=$\sqrt{(103)}$

R=10.15m/s

the direction

tan$\alpha$=TUy/TUx

tan$\alpha$=4.7/9

$\alpha$=tan^-1(0.522)

$\alpha$=27.57deg