10) A professional fireworks team shoots an 8-in. mortar straight upwards from ground level with an initial speed of 256 ft/sec. a. Write a function modeling the vertical position s(t)(in ft) of the shell at a time t seconds after launch. b. The spectators can see the shell rising once it clears a 768-ft tree line. From what period of time after launch is the shell visible?

1. 3.A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter's frame of reference. (b) What is its average velocity over one revolution? 2. Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain. 3. A commuter backs her car out of her garage with an acceleration of (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.800 s, what is her deceleration

Geese migrate along north and south directions for well over a thousand kilometers in some cases traveling speeds up to about 100 km/h. If one such bird is flying at 100km/h relative to the air but there is a 34.0 km/h wind blowing from the west to east. A.) at what angle relative to the north-south direction should this bird head so that it will be traveling directly southward relative to the ground? Express answer in degrees  b.) how long will it take the bird to cover a ground distance of 500 km from north to south? ( Note: Even on cloudy nights many birds navigate using the earth's magnetic field to fix the north-south direction)

5. A projectile is launched at an angle of 50° with the horizontal and a speed of 25 m/s. a) What is the Range of the projectile? b) What is its height after 1.5 second?

Whale sharks swim forward while ascending or descending. They swim along a straight-line path at a shallow angle as they move from the surface to deep water or from the depths to the surface. In one recorded dive, a shark started 50 m below the surface and swam at 0.85 m/s along a path tipped at a 13° angle above the horizontal until reaching the surface. a. What was the horizontal distance between the shark's starting and ending positions?

A ball is thrown at an initial height of 90 feet at an initial velocity of 55 feet/second at an angle of 75 degrees. Given the parametric equations y = 16t2 + Vo · Sin(0)t + ho and r = Vo Cos(0)t. When doing calculations, carry 5 digits of accuracy, so your round off does not build up. a. What is the ball's height in 3 seconds? feet. b. When will the object hit the ground? seconds. c. How far horizontally will the ball be when it hits the ground? feet. d. When will the ball be at its maximum height? seconds. e. What is the ball's maximum height? feet. f. How far horizontally will the ball be when it reaches its maximum height? feet

For A,B,and C

5. The x-location and y-location of a particle are described by the following equations, where x and y are in meters and time is in seconds: x = 4e-t y = 2 + 8e -2t a. What is the equation of the particle's path in the x-y plane? b. What are the (x,y) coordinates of the particle at time=0 and as time → ∞o? c. What is the speed of the particle at time=0?

Please help, thank you.