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For a falling object, say a ball, which bounces, what would be the expected shape of the vertical position (y-axis) vs time (x-axis) graph.
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- The horizontal distance or range (R) of an object thrown at an angle θ from the horizontal is represented by the equation below where v0 is the initial velocity as the object leaves the hand, in feet per second. If v0 = 2500 feet per second and θ is changed from 13° to 14°, use differentials to approximate the change in range, in feet.A rocket's position (in meters) as a function of time (in seconds) is given below. Round all answers in this problem to one decimal place r² = (t² − 3t)i + (t³ + 3)ĵ (a) What is the magnitude of the rocket's (in m/s) velocity at t = 2.5 s? (b) In what direction is the rocket moving (in degrees) at t = 2.5 s? (c) What is the magnitude of the rocket's acceleration (in m/s²) at t = 2.5 s?A projectile is fired from the top of a ridge and its height is given by the equation s(t) =-16t² +70t + 5. Write a sentence, including units, explaining the time interval for which the projectile will be above 60 feet in the air. Round values to the nearest tenth.
- In an experiment, a student launches a ball with an initial horizontal velocity of 5.00 meters/sec at an elevation 2.00 meters above ground. Draw and clearly label with appropriate values and units a graph of the ball's horizontal velocity vs. time and the ball's vertical velocity vs. time. The graph should cover the motion from the instant after the ball is launched until the instant before it hits the ground. Assume the downward direction is negative for this problem.On a day when the wind is blowing toward the south at 4 m/s , a runner logs west at 1.6 m/s s.what is the magnitude of of the air relative to the runner Calculate answer to one decimal.The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, answer the following. (a) Determine the initial speed of the projectile.m/s(b) Determine the total time the projectile was in flight.s(c) Qualitatively, how would the answers change if the launch angle were greater than 45°? Explain.
- A cork bobs up and down in a lake. The distance from the bottom of the lake to the center of the cork at time t>=0 is given by s(t)= 25+cos(pi t), where s(t) is in feet and t Is in seconds. During what time interval is the cork rising. Draw pictures as wellIf you plot R (on the y-axis) vs. sin(20) (on the x-axis), you get a linear graph. Mathematically, how is the slope of this graph related to the launch speed?Consider the game of baseball. A pitcher throws a ball to the catcher, with a speed of 86 miles per hour (38.45 m/s). If the velocity of the ball is horizontal when it leaves the pitcher's hand, how far (vertically) will it fall on the way to the catcher? The distance from the pitcher to the catcher is 57 feet (the pitching distance used from 1890 to 1893). Express your answer in meters and feet. m ft