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Question

goku and piccolo are at a 90 degree angle from each other, facing Raditz. Raditz is confidently standing still, thinking no earthlings can defeat him. goku unleashes a kamehamaha which travels at 1000mi/s, and piccolo fires off a masenko wave at 1500 mi/s. at what rate is the angle between goku and the masenko wave changing when the masenko beam is .4mi from Raditz if goku is standing .3mi from Raditz? (hint: draw a triangle and use trig)

Answer 1

G

↓|\

|θ\

.3| \

| \

|____\

R x P

←

dx/dt = -1500 mi/s

tan(θ) = x/.3

Take derivative of both sides

sec²(θ) dθ/dt = (1/.3)dx/dt

dθ/dt = (1/,3)(1/sec²(θ))dx/dt = (1/.3)cos²(θ) dx/dt

when the masenko beam is .4 mi from Raditz, it forms a .3-.4-.5 triangle, so cos(θ) = .3/.5

dθ/dt = (1/.3)(.3/.5)²(-1500) = (.3/.25)(-1500) = -1800 radians/sec (decreasing)

The kamehamaha velocity is not needed