In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat the athlete as a particle and let ymax be his maximum height above the floor.To explain why he seems to hang in the air, calculate the ratio of the time he is above ymax/2 (moving up from ymax/2 to ymax and then moving down to ymax/2) to the time it takes him to go from the floor to that height. You may ignore air resistance.

At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of vo = i+ 5j – k. The acceleration function of the particle is a(t) = 32r²i + j+ (cos 21)k. Find the speed of the particle at time t = 1. Round your answer to two decimal places.

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

uber eats driver-completes her route by traveling 167 m in a direction 30⁰ north of east, 140 m 20 ⁰ west of north, and then 180 m west. What is her final location (magnitude and direction) relative to her starting location?

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 20 ft/s. 90 ft (a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) ft/s (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.) ft/s Need Help? Read It

A skater with mass 66 kg is skating on a horizontal surface at a constant speed 4.2 m/s. There is a ramp ahead, and the skater has just enough speed to make it to the top of the ramp (meaning the speed at the top of the ramp is 0 m/s). What is the height of the ramp in the unit of meters? Use g = 10 m/s2 for the acceleration due to gravity.

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 46 ft/s. Its height in feet after t seconds is given by y = 46t – 21t2. A. Find the average velocity for the time period beginning when t=2 and lasting .01 s: .005 s: .002 s: .001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. Estimate the instanteneous velocity when t=2.

How would  I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)

Riding up an escalator while staying on the same step for the whole ride takes 29 s . Walking up the same escalator takes 20 s. If you are walking against the escalator and you are at the top of the escalator right now, how many seconds ago were you at the bottom? Express your answer with the appropriate units.

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