
11. The height of a projectile is modelled by the function h(t) = -4.912 + 25.5t...
A skydiver jumps out of a plane. The height of a skydiver can be modelled by the quadratic function () = -4.912 + + + 4900, where t is the time in seconds and h, is the height above the ground in metres. After he releases his parachute, his height above the ground can be modelled by the function h (1) -- 51+ 4100. How long after jumping did he release his parachute? (3 marks)
The height of a ball thrown vertically upward from a rooftop is modelled by y=-5t^2+20t+50 , where h(t) is the ball's height above the ground , in meters , at time t seconds after the throwa) Determine the max height of the ballb) how long does it take for the ball to reach its max heightc) How high is the rooftop
5. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modelled by h(t) -5t-5t+180 where h is the height in metres at t seconds since the pebble started to fall. a. Find the average rate of change between 1 s and 4 s. b. Find h(3) c. Find the instantaneous rate of change of height at 3 s. d. Explain the meaning of each value calculated in parts...
a flare is fired from the deck of a sinking ship. Its trajectory can be modelled by the function h(t) = -4.9t^2 + 92t where h is the height of the flare in meters and t is the time in seconds. A seagull is flying 100m above the sinking ship. How long will the flare be above the bird if it continues to fly at the same height?
A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi. (a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height. t = (b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained...
4. (11 marks] If the height above sea level is given by the function H(x,y) = 100+ (x + 1)?y2 and r(t) = 2t i++) is a path through the landscape, use the chain rule to find the lowest and highest points on the path between t = -1 and t = 1. (Don't forget to consider the end points)
An airplane is flying at a height h, above the ground when it shoots a projectile with v. = 80 m/s at 24° below the horizontal as shown in the figure. Please assume that the projectile is in free fall while it is in the air. a) How long would it take for the projectile to accelerate to a speed of 110 m/s? b)lf the package lands 1 km from where it was shot, at what height is the plane...
The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation:h= 10 sin ((pi/15 t) - 7.5) + 12 where t is the time, in seconds.At t=0, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.
1. The position function of a projectile is given by: r(t) = (5.0 t + 6.0 t2) m i + (30 – t3) m j From what height above the ground was the projectile launched? What is the displacement of the particle in magnitude angle form at t = 2.0 s? What is the time taken for the projectile to land on the ground? What is the horizontal displacement of the projectile when it lands on the ground? What...
A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi. (a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height. (b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the...