Answer to Question #80921 in Physics for Sidra Madeeha Ahmad

Question

One of the games at the Rec Room is a giant, square air hockey table with side length s=2.00 m. On the air hockey table, pucks slide across a horizontal table with effectively no friction (for the purposes of this problem). At time t=0 s a puck is launched from the corner at an angle of θ = 30.1° with respect to the bottom edge of the table with a speed of v1 = 0.314 m/s. At the same time, you launch another puck from an adjacent corner at an angle φ=30.5° at a speed so that the pucks will collide. How long after launch will the collision happen? You can assume the pucks have negligible size. Express your answer in seconds to three significant figures

Answer 1

"AAS" means "Angle, Angle, Side"
To solve an AAS triangle
use the three angles add to 180° to find the other angle
then The Law of Sines to find each of the other two sides.

In this triangle we know:
angle θ = 30.1°
angle ϕ=30.5°
and side s = 2.00

It's easy to find third angle by using 'angles of a triangle add to 180°':
β=180°-30.1°-30.5°=119.4°

We can also find side a=v_1 t by using The Law of Sines:
a/sin⁡φ =s/sin⁡β
a=s sin⁡φ/sin⁡β =2.00×sin⁡〖30.5°〗/sin⁡〖119.4°〗 =1.165 m
So,
v_1 t=a
t=a/v_1 =1.165/0.314=3.71 s