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- 3. A satellite is launched from the surface of the earth at the initial speed of 8 km/s. How high will it go before it stops and starts falling back to the earth?4. Given the path, find a decomposition of the acceleration vector à(t) into tangential and normal components at the point indicated. T(t) = (cos t, sin t, t) : at t = T1. A rock is thrown off a cliff at an angle of 51 with respect to the horizontal. The cliff is 126 m high. The initial speed of the rock is 24 m/s. (a) Fill in the following: Vo Vox Voy || || ✓ m S ES = ES m (b) VX (c) V (d) In your notebook, draw a sketch of the problem. Select the direction along the along the vertical axis (y-axis) that is positive (upwards or downwards). Select the direction along the along the horizontal axis (x-axis) that is positive (left or right). Select an origin. Draw the vectors for Vo, Vox Voy" V, Vx, Vy, ax, a¸. Label on your diagram the initial and final positions of the rock x, y, and xƒ‚ Yf. (e) How high above the edge of the cliff does the rock rise? Ay= m 00 (f) How far has it moved horizontally when it is at maximum altitude? Δx= m (g) How long after the release does it hit the ground? ground= (h) What is the range of the rock? Ax total ✔m S (i) What are the horizontal and vertical positions of the rock relative to the edge of the cliff at t = 4 s.…
- The acceleration of a free falling body is described by a = 9.81 [1-10-4. v²] m/sec², where v is in m/sec and the positive direction is downward. If the body is released from rest at a high altitude, calculate the velocity when t = 5 sec in m/sec using the formula below. I In/a+x\ + C dx 1 2 2 S a²-x² 2a la-x, for a²x², where a and c are constants .12. An airplane turns slowly for 9.2 s horizontally. The final velocity of the plane is 3.6 X 10 km/h [N]; the average acceleration during the turn is 5.0 m/s [W]. What was the initial velocity of the plane? AW Mot X DThe X G dece X x C G dece x S S Stud X E Grac X Grac XE Grac X G mot X G net X G g to X Revi X a classroom.google.com/u/0/c/M]Y4MTUXMDQ3MZQZ/a/MzExODMzNzQwOTQw/details c) What is the average velocity of each car for the first 10s? 4. A car is travelling at 10 m.s when the driver sees a police car. The driver brakes and decelerates at 4 m.s for 2 seconds. After 2 seconds of braking, the driver is confident that the police have not seen him so speeds up again to his original speed in 4 seconds and then maintains his original speed. 10 6. 8. 7. 5. 41 2. 1. 0 1 2 3 4 5 Time (s) a) What is the acceleration when the driver is speeding up again? 9. 7 8 9 10 b) What is lowest instantaneous velocity of the car and at what time does it occur? c) What is the displacement of the car travel under braking? Type here to search 6, 3. Velocity (m/s)
- find the instantaneous acceleration at t= 0.55 s given the displacement equation: x= t^4 - 2.8t^3 + 3.1t^2 + 4.4t -9.54. Given the acceleration as a function of the angle theta, a = 6.5 sin θ + 2.3cos θ i. Find the optimal angle, so the acceleration is maximum. ii. Find the value of the maximum acceleration.4. Assume a 5-m ladder sliding down a wall. The variable h is the height of the ladder’s top at time t, and x isthe distance from the wall to the ladder’s bottom. Assume the bottom slides away from the wall at a rate of0.8m/s. Find the velocity of the top of the latter at t = 2s if the bottom is 1.5m from the wall at t = 0s.