26. 017 POINTS PREVIOUS ANSWERS The height of a cannonball is h(t) - - 1662 +64...
A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 24 ft from the house, the base is moving away at the rate of 7 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between...
9. (5 points) A 10 feet long ladder that was leaning against the wall as shown below. A guy was pushing the lower end of the ladder toward the wall and his action made the top end of the ladder moving up against the wall at the rate of 4 feet per second. How fast was the lower end of the ladder moving toward the wall when the lower end was 8 feet away from the wall? and at the...
4. (5 points) Related Rates. A 17 ft. ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 5 ft/s, how fast will the top of the ladder be moving down the wall when it is 8 ft. above the ground? 5. (5 points) Find the absolute maximum and absolute minimum of f(x)= 3x4 – 4x' on the interval (-1,2]. Use calculus and show...
(1 point) Consider a cannonball launched along the path p(t) (400t + 70, 300t – 350, 37t – 16t?), with length units in feet and time units in seconds. When does it return to the height from which it was launched? (The coordinate system is right-handed, with z the vertical axis.) Answer: t= What is its velocity then? Answer: kg ft kg m s but here we can measure it in Momentum is mass times speed, usually measured in impact...
7. 12.22 points SCalcCC4 4.1.023 My Notes Ask Your Teacher The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.3 m/s. How long is the ladder? Need Help? Read It Talk to a Tuter 8.12.22 points SCakCC4 4.1.029 My Notes Ask Your Teacher Gravel is being dumped from...
A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by h= -16t^2+32t+3584. What is the rocket's maximum height? ___ ft How long does it take for the rocket to reach its maximum height? t= ___sec After it is fired, the rocket reaches the ground at t= ___ sec.
1. If a ball is thrown vertically upward with a certain velocity, its height (in feet) after t seconds is s(t) = 28t - 4tº. Answer the following questions with correct units. (a) Find the velocity and acceleration of the ball after 2 sec? (b) What is the maximum height reached by the ball? (c) Determine the velocity of the ball when it hits the ground. 4 6 6 6 6 2. Find the derivatives of the following functions. You...
Problems 27-28. Sketch the graph of the quadratic function. Label the vertex and two additional points. 27) f(x) +4x-3 28) gx) 20+4)-3 10 10 10 x 10 510x -10 -5 10 1of -10 29) Standing atop a 64-foot platform, Susan throws a softball into the air at an initial speed of 48 feet por second. The distance above the ground h at t seconds is given by h-16t2 +48t 64. a) Find the height of the softball after 2 seconds....
2. +0/3 points | Previous Answers 4/7 Submissions Used My Notes The height of a helicopter above the ground is given by h 2.95t3, where h is in meters and t is in seconds. Att2.05 s the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground? [HINT: Make a list of important clock readings. Make a motion map for the bag before and after it is dropped. Make a list of known quantities....
If an object is thrown upward with an initial velocity of 64 ft/sec, its height after t sec is given by h = 64t -16t^2. Find the number of seconds the object is in the air before it hits the ground.