Determine the drag coefficient ca needed for a parachutist of mass m = 68.1 kg to have a velocity of 40 m/s after free-falling for time t = 10 s. Assume the acceleration due to gravity is 9.8 m/s². gm v(t) = "[1- Ca
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- Vmax In a laboratory experiment, a sphere of diameter 8.0 mm is released from rest at t = 0 at the surface of honey in a jar, and the sphere's downward speed v when it travels in the honey is found to be given by v = Vmax (1 - e-t/T), where 0.040 m/s and T = 0.50 s. (a) Obtain an expression for a(t). (b) Draw graphs for v(t) and a(t) for the time interval 0 to 2.0 s. (c) Obtain an expression for x(t), choosing the positive x axis as downward, and draw the graph for this func- tion. (d) Use your x(t) graph to determine the time interval needed for the sphere to reach the bottom of the container if the surface of the honey is 0.10 m above the bottom of the jar. ... =A 1.80x10^4 kg semi-trailer truck drives up a 200 m hill [θ = 30 degrees above horizontal], at a constant speed of 25.0 m/s. The force of friction is 6.00x10^2 N. Write an equation to isolate and solve for P.A space shuttle lands on a distant planet where the gravitational acceleration is 2.0 ( We do not know thelocal units of length and time , but they are consistent throughout the problem). The shuttle coasts along aleve, frictionless plane with a speed of 6.0. It then coasts up a frictionless ramp of height 5.0 and angle 0f 30°.After a brief ballistic flight, it lands a distance S from the ramp. Solve for S in local units of length. Assume theshuttle is small compared to the local length unit and that all atmospheric effects are negligible. Use x and y components.
- According to Newton's Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from the earth's surface is mgR? F = (x + R)- where x = x(1) is the object's distance above the surface at time t, R is the earth's radius, and g is the acceler- ation due to gravity. Also, by Newton's Second Law, F = ma = m(dv/dt) and so dv m dt mgR? (x + R)? (a) Suppose a rocket is fired vertically upward with an initial velocity vo. Let h be the maximum height above the surface reached by the object. Show that 2gRh VR+ h [Hint: By the Chain Rule, m (dv/di) = mv (dv/dx).] (b) Calculate v. = lim--- Vo. This limit is called the escape velocity for the earth. (c) Use R = 3960 mi and g = 32 ft/s² to calculate v, in feet per second and in miles per second.The model for this set of velocity data is given by: v(t) = [(1100/3)e^(-0.03t)] - (462/5) Use this model to calculate the instantaneous acceleration at t = 15, t = 25, t = 35, and t = 45 seconds. Use this model to calculate the total distance traveled at t = 15, t = 25, t = 35, and t = 45 seconds.The CERN particle accelerator is circular with a circumference of 7.0 km. (a) What is the acceleration of the protons (m = 1.67 × 10-27 kg) that move around the accelerator at 5% of the speed of light? (The speed of light is v = 3.00 × 108 m/s.)
- magnitude gravitational force (between a planet with mass 9.00 * 10 ^ 24 and moon, with 2.40 * 10 ^ 22 average distance between their canters 2.10 * 10 ^ 8* m b) ? is the moon's acceleration in m/s^ 2 ) toward the planet(Enter the magnitude. ) m/s^ 2 the planets acceleration (in m/s^ 2 ) the moon?What is the value of g at an altitude of 12,000 km above Earth's surface? Consider: rEarth = 6.38 x 106 m MEarth = 5.98 x 1024 kg Give your answer in m/s/s to the correct number of significant figures.The Sun orbits the center of the Milky Way galaxy once each 2.60 × 108 years, with a roughly circular orbit averaging 3.00 × 104 light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the average speed of the Sun in its galactic orbit in m/s.
- m m 2 Traveling with an initial speed of 128 kr, a Cessna 172 accelerates at 6000kr during level flight. How long will it take to reach a speed of 226kr ? Give your answer in seconds (s).A 40-lb suitcase slides from the rest 20 ft down the ramp. The suitcase has an initial velocity down the ramp of v_A = 13 ft/s and the coefficient of kinetic friction along AB is μk = 0.25. (a) How long does it take to go from A to C? Express your answer to three significant figures and include the appropriate units. Answer is not 1.264s (b) Determine the point where it strikes the ground at C. Express your answer to three significant figures and include the appropriate units. Answer is not 5.348 ftFor a mass m falling in air, we assume that the air resistance is proportional to the speed v (t): mv '(t) = mg - kv (t),where g is the acceleration of gravity and k is a positive constant that depends on the geometry of the object.What is v (t) given that v (0) = 0?