s(a) – s(t) lim а — t
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Use the position function s(t) = −16t2 + 500, which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by as attached. A construction worker drops a full paint can from a height of 500 feet. When will the paint can hit the ground? At what velocity will the paint can impact the ground?
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- A dart gun contains a spring of spring constant k = 16 N/m which is used to shoot a dart of mass m. The dart leaves the gun at a speed of v = 3.1 m/s after the spring is compressed 1 cm. what is the darts speed when it hits the floor (vf in m/s) if it is fired horizontally at a height of h = 2 m what angle in degree does the darts final velocity make with the horizontal?A silver dollar is dropped from the top of a building that is 1345 feet tall. Use the position function below for free-falling objects. s(t) = -16t2 + vot + so (a) Determine the position and velocity functions for the coin. s(t) = v(t) = (b) Determine the average velocity on the interval [1, 2]. ft/s (c) Find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/sNASA has fired a rocket straight up into the air from ground level with an unknown initial velocity. It reaches a maximum height of 164,000 feet. This happened in Cape Canaveral therefore the rocket is under the acceleration of Earth's gavity in which we all know is -32 ft/sec/sec. Please round your answers to two decimal places. a). Find the time it takes for the rocket to reach maximum height. b). find the initial velocity necessary to reach that height.
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- The height above the ground of a drone is given by h = 3.50 t³, where h is in meters and t is in seconds. Calculate at t = 2.50 s (a) the height of the drone above the ground and (b) the velocity of the drone. At this time (t = 2.50 s) the drone releases a package (c) how long does it take the package to reach the ground? Include a complete diagram of the situation.A helicopter starts ascending in the sky from the ground and its position is given by 5t2 + 10t. After 10 seconds, a package is dropped out from the helicopter. What is the velocity of the package when it descends to a height of 10 m above the ground. Y =