1) A security car with its spotlight on is parked 40 meters from a warehouse. Consider θ and x as shown in the figure. Write θ as a function of x.
2) A weight is oscillating on the end of a spring (see figure). The position of the weight relative to the point of equilibrium is given by
y = 1/14(cos9t - 3sin9t)
where y is the displacement(in meters) and t is the time (in seconds). Find the time when the weight is at the point of equilibrium (y = 0) for 0 ≤ t ≤ 1.
3) The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by:
d= (v2/32)sin2θ
where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 100 feet per second when the ball is hit at an angle of θ = 40°. Round to the nearest foot.