2. Suppose we now have a little ball bouncing vertically and lightly on the trampoline. The ball's mass is 0.5kg. Air resistance is unchanged. At time t = 0, the ball again starts at height 0.6 m above the ground and the velocity of the ball is 0. Draw a graph of h(t) in this case and briefly explain your reasoning. Hint: you do not need to solve for y(t).
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- A 0.26-kg rock is thrown vertically upward from the top of a cliff that is 32 m high. When it hits the ground at the base of the cliff, the rock has a speed of 31 m/s. A) Assuming that air resistance can be ignored, find the initial speed of the rock. Express your answer using two significant figures. B) Find the greatest height of the rock as measured from the base of the cliff. Express your answer using two significant figures.D Two cannons aimed directly at each other fire simultaneously. The cannon balls have the same speed immediately after being fired. Some time later, the cannon balls collide at point P. xe increases as H decreases H How does xe, the horizontal distance from the edge of the building to where the cannon balls collide, depend on the height of the building H? xe does not depend on H xe decreases as H decreasesA particle moves along the x-axis according to r(t) = 4t - 7t² m. a. What is the instantaneous velocity at t 3 s? m/s b. What is the instantaneous speed at t = 3 s? m/s c. What is the average velocity between t = 2 s and t = 3 s? m/s
- At t=0, a particle starts from rest at x= 0, y = 0, and moves in the xy plane with an acceleration a = (4.0₂ + 3.0)m/s². Assume t is in seconds. Part C Determine the speed of the particle as a function of time t. Express your answer using two significant figures. ΜΕ ΑΣΦ v(t) = Submit Request Answer Part D ? m/s Determine the position of the particle as a function of time t. Express your answer using two significant figures. Express your answer in terms of the unit vectors i and ĵ. ΑΣΦ F(t) = ? mA car is driving along a circular track of diameter d = 0.75 km at a constant speed of v = 22 m/s.a. Write an expression for the magnitude of acceleration a of the car in terms of the given parameter. b. What is the magnitude, in meters per second squared, of the acceleration a of the car. c. Write an expression for the minimum coefficient of the friction μ between the car's tires and the road that is required in order to keep the car going in a circle in terms of the given parameters.In 2070, Adam wins a vacation at the new Moon Country Club. While vacationing Adam hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45° to the horizontal on the Moon(gravity on the Moon is one-sixth of that on Earth). Round all answers to three decimal places. a. Find parametric equations that describe the position of the ball as a function of time, t (round coefficients to three decimal places). b. How long is the ball in the air? c. When is the ball at its maximum height? What is that maximum height? d. When the ball lands, how far is it from Adam(the horizontal distance the ball traveled)?
- 201d. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 18.5 m/s. The cliff is h = 20.0 m above a flat, horizontal beach as shown in the figure. Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x= y=Two spheres are launched horizontally from a 1.2 mm -high table. Sphere AA is launched with an initial speed of 4.5 m/sm/s . Sphere BB is launched with an initial speed of 2.5 m/sm/s . A. What is the time for the sphere AA to hit the floor? Express your answer using two significant figures. B. What is the time for the sphere BB to hit the floor? Express your answer using two significant figures.
- A particle P starts at time t = 0 s at the polar position x = -15 m y = 8 m. The velocity of the particle is written in the polar basis associated with its current position, and is: v = 2ê, m/s. If we have final and final, then we can find final and final with: X final symbolic expression X = ? m, yfinal ? Give your answers in symbolic form. You should use the scalar variables r_f and theta_f. Functions are available like sin(), cos(), atan2(), sqrt(), and log(), as well as the mathematical constants pi and e. The regular arithmetic operators are +, -, *, and /, and x^y means x to the power of y. 5t + k would translate to 5*t+k. Now, find the final Cartesian position of the particle at time t = 2. symbolic expression m, y = ? m mA ball is suspended from a light 1.2 m string as shown. The string makes an angle of 27 degrees with the vertical. The ball is then kicked up and to the right such that the string remains taut the entire time the ball swings upwards. This kick gives the ball an initial velocity of 1.1 m/s. PART A. What will be the speed, in meters per second, of the ball when it reaches its lowest point (θ = 0)? PART B: What will be the speed, in meters per second, of the ball when it reaches its lowest point (θ = 0)?You are on the planet Neptune and want to determine the acceleration due to gravity, g. You have a stopwatch and a toy gun that can launch a ping pong ball vertically upwards with an initial velocity of 7.5 m/s. Describe, in words, how you would perform an experiment to determine the acceleration due to gravity. Be sure to describe the variables you would measure, the equations you would use and the assumptions you would make. Make sure to include a diagram of the physical situation, label the unknown and known quantities with units, coordinate system in your answer.