Question #1: An experimental railgun fires a steel slug into a resisting medium for impact analysis. The steel slug hits the medium's surface at 900 [ft/s]. After impacting, the steel slug penetrates 4 [in] in the medium. The medium surface is defined as x = 0 . The velocity of the steel slug was experimentally determined to be (v = vo – kx) [ft/s]. Determine: a) The initial acceleration of the steel slug immediately after it hits the medium b) The time it takes for the steel slug to penetrate exactly 3.9 [in] Use the following diagram. X = 0 Vinitial Resisting Medium
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- The speed of propagation of the action potential (an electric signal) in a nerve cell depends (inversely) on the diameter of the axon(nerve fiber). If the nerve cell connecting the spinal cord to your feet is 0.9 m long and the nerve impulse is 16 m/s. How long (in s) does it take for the nerve signal to travel this distance ?If you make multiple measurements of your height, you are likely to find that the results vary by nearly half an inch in either direction due to measurement error and actual variations in height. You are slightly shorter in the evening, after gravity has compressed and reshaped your spine over the course of a day. One measurement of a man's height is 6 feet and 1 inch. Express his height in meters, using the appropriate number of significant figures.Meanwhile at the ballpark Juan was practicing his hitting while talking to some friends. He started telling them how he hit the ball over the 50 foot light tower yesterday. The formula for this hit is , h(x)=-16x^2+60x+4, where h is the height of the ball and x is the number of seconds the ball is in the air. 1. How can Juan provide proof to the friends that he actually hit the ball over the tower? 2. How high did Juan actually hit the ball? Is Juan able to mathematically back up how high he says he hit the ball?
- = A polo ball is hit with a mallet off the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 16.8t and y meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r= By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) m (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² II m/s to || (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the polo ball at t = 2.85 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) 3 3.72t - 4.90t2, where x and y are in m/s m/s²The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.According to Los Angeles Air Traffic Control, an Air Force SR-71 has a constant velocity of 1942 knots (999 m/s) along the negative y direction, and a Navy F-18 has an acceleration of 4 m/s^2 along the positive x direction (both of these are fighter jets). What is the acceleration of the F-18 as measured by an observer in the SR-71 (in m/s^2)? [i and j represent unit vectors along the x and y directions respectively]
- A car is traveling at a speed of 29 m/s on an interstate highway where the speed limit is 76 mi/h. Is the driver exceeding the speed limit? What is the car's speed in mi/h? Observe correct number of significant figures in your final answer.Given the quantities a = 4.6 m, b = 4.4 s, c = 75 m/s, what is the value of the quantity d = cb² Number i 0.06 Units m/s^2 ?An object's velocity as a function of time in one dimension is given by the expression; v(t) = 3.8t + 6.68 where are constants have proper SI Units. At what time is the object's velocity 61.2 m/s?
- help answer please.The students in this class performed an experiment to determine the acceleration of a ball due to gravity. Their average results were 9.86 m/s^2. the actual acceleration due to gravity is 9.81 m/s^2. what is the percent error for this experiment?After conducting the signal speed experiment a student has recorded the following data. L₂ (m) 1.5 3 4.5 8 15 30 dt (ns) 6.50 13.72 21.02 38.10 72.20 145.42 L2 is the length of the longer cable in meters and dt is the measured time delay in nanoseconds. The student neglected to record L₁, the length of the shorter cable. After speaking with their instructor, they learn all is not lost. They know the speed of the signal can be calculated based on the distance traveled divided by the time. However, the recorded times measure how much longer the signal had to travel in L2 compared to L₁. A little bit of thought convinces them (correctly) that