A baseball player stands 5 meters from home plate and watches a pitch fly by. In the diagram, x is the distance from the ball to home plate and is the angle indicating the direction of the player's gaze. Find the rate at which his eyes must move to watch a fastball with x '(t)=-45 m/s as it crosses home plate at x = 0. rad/s. Plate 5 Player

How fast is the tip of her shadow

whats y" of y=15xcosx

You car is moving along in cruise control at a constant speed of 88.3 ft/s (about 60 mi/hr).  A text message appears on your phone and you look down to read it.  When you look back up at the road, you see a car at a complete stop in your lane 156 ft ahead of you.  It takes 0.39 s for you to react and apply the brakes.  When the brakes are applied your car experiences an acceleration of -32.3 ft/s2.  Fortunately, you are able to avoid hitting the other car.  What is the distance between the two cars when you come to a complete stop? (0.9 ft).

Find the distance between -4 u = -5 and z = 2 8.

A projectile is given an initial velocity of 31.5 m/s at an angle of 51.5 degrees with respect to the horizontal. How far has it moved in the x-direction at the time when its speed in the y-direction is 10.5 m/s? A projectile is launched with an initial velocity of 27.2 m/s at 64.7 degrees with respect to the horizontal. What is the speed of the projectile 1.83 s after being launched. Assume the speed is measured in m/s.   A projectile is launched with an initial velocity of 46.8 m/s at an angle of 31.2 degrees with respect to the horizontal. In meters, what is the maximum upward displacement of the projectile?

A rocket has taken off and is rising vertically according to the position equation, s = 50t^2 (use this to find the “given” rate of change). It is being tracked by a device located 2000 ft from the point of lift-off. The angle θ (in radians) is the angle between the tracking line and the ground. Find the rate of change in the angle θ , 10 seconds after lift-off.(a) GIVEN: Use the position function to find the given rate of change at t = 10 sec.(b) FIND: Write the derivative you want to find.(c) Write an equation relating the variable θ and two sides of the triangle. Then, differentiate with respect to time. (d) Solve for the unknown derivative in (b) after substituting in known values. Note: first you will need to solve for both s and the length of the hypotenuse at t = 10 sec.. Use a calculator for your final computations.