Quadratic Functions
Ali and Steven walk up a mountain and drop a ball from the edge of a cliff. The height of the ball can be modelled by the function h(t) = -5t2 + 80 where h(t) is the height of the ball above sea level, in metres, at time t seconds after it is dropped.
b) Determine the equation for h-1(t).
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Ali and Steven walk up a mountain and drop a ball from the edge of a cliff. The height of the ball can be modelled by the function h(t) = -5t2 + 80 where h(t) is the height of the ball above sea level, in metres, at time t seconds after it is dropped.a) Determine the domain and range of the function.
Ball has initial velocity v m/s in x direction Cliff Ball strikes sea at point (s,0)...
Ball has initial velocity v m/s in x direction Cliff Ball strikes sea at point (s,0) Sea (0,0) 3(c) [7 Marks] A golf ball is struck with velocityv (meters per second) from the edge of a cliff which rises h metres above sea level. Referring to figure (3) the golf ball starts at the point (0, h) follows a parabola and strikes the sea some time later at the point (8,0). It can be shown that the (x, y) location...
A ball is launched into the air from below a cliff, such that after t seconds...
A ball is launched into the air from below a cliff, such that after t seconds its height above the cliff top is h metres, and is given by the equation h 4.9t219.6t -9.6 Calculate, to the nearest metre, the maximum height the ball achieves above the cliff top Enter your answer below, as a number without units.
A skydiver jumps out of a plane. The height of a skydiver can be modelled by...
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)
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...
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...
From a clifftop over the ocean 592.9 m above sea level, an object was shot straight up into the a...
From a clifftop over the ocean 592.9 m above sea level, an object was shot straight up into the air with an initial vertical speed of 94.08 ms. On its way down it missed the cliff and fell into the ocean, where it floats on the surface. Its height (above sea level) as time passes can be modeled by the quadratic function f, where f(t)=−4.9t2+94.08t+592.9. Here t represents the number of seconds since the object’s release, and f(t) represents the...
The pathway of a ball thrown in the air is modelled by the equation 5y =...
The pathway of a ball thrown in the air is modelled by the equation 5y = - 4x2 + 40x, where y represents the ball's height in metres after x seconds. The ball will reach its highest point at the vertex. a) Solve the equation - 4x² + 40x = 0 and hence find when the ball strikes the ground. (b) Find the vertex of your equation. c) Graph your function. (d) Find the maximum height that the ball will...
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
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.
The maximum height of water near a tidal power station in New Brunswick is 6.4 metres...
The maximum height of water near a tidal power station in New Brunswick is 6.4 metres at 4:30 am and the minimum height is 3.6 m, 6.2 hours later. What is the depth of the water at 6:45 pm? a) 2.8 m b) 6.8 m c) 5.8 m d) 5.0 m A ferris wheel at an amusement park completes two revolutions every 120 seconds. The cars can reach a maximum of 10 metres above the ground and a minimum of...
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 throw a) Determine the max height of the ball b) how long does it tak
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
Ball has initial velocity v m/s in x direction Cliff Ball strikes sea at point (s,0) Sea (0,0) 3(c) [7 Marks] A golf ball is struck with velocityv (meters per second) from the edge of a cliff which rises h metres above sea level. Referring to figure (3) the golf ball starts at the point (0, h) follows a parabola and strikes the sea some time later at the point (8,0). It can be shown that the (x, y) location...
A ball is launched into the air from below a cliff, such that after t seconds its height above the cliff top is h metres, and is given by the equation h 4.9t219.6t -9.6 Calculate, to the nearest metre, the maximum height the ball achieves above the cliff top Enter your answer below, as a number without units.
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)
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...
The pathway of a ball thrown in the air is modelled by the equation 5y = - 4x2 + 40x, where y represents the ball's height in metres after x seconds. The ball will reach its highest point at the vertex. a) Solve the equation - 4x² + 40x = 0 and hence find when the ball strikes the ground. (b) Find the vertex of your equation. c) Graph your function. (d) Find the maximum height that the ball will...
The maximum height of water near a tidal power station in New Brunswick is 6.4 metres at 4:30 am and the minimum height is 3.6 m, 6.2 hours later. What is the depth of the water at 6:45 pm? a) 2.8 m b) 6.8 m c) 5.8 m d) 5.0 m A ferris wheel at an amusement park completes two revolutions every 120 seconds. The cars can reach a maximum of 10 metres above the ground and a minimum of...
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