Question

8. [Sec. 10.91 A ball is thrown eastward into the air from the origin (in the direction of the positive r-axis). The initial velocity is 50i 80k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4 fus2, so the acceleration vector is a-4j - 32k. Find the following (a) The coordinates of the point where the ball lands. (b) The distance (round your answer to the nearest foot) from the origin to the point where the ball lands. (c) The angle (round your answer to the nearest degree) between the positive r-axis and the vector to the point where the ball lands. (d) The speed (round your answer to the nearest fus) at which the ball strikes the ground. 9. [Sec. 10.91 An automobile travels at a constant speed around a curve whose radius of curvature is 1000 m. What is the maximum allowable speed if the maximum acceptable value for the scalar component of the normal acceleration is 1.5 m/s22 Round your answer to 2 decimal places.

Answer 1

Given that: The velocity at origin = 50 i + 80 k The acceleration of ball = -4j - 32 k As we know, when the ball land the height of ball = 0 which means k = 0 And the motion of ball land (&) ground, depands on the velocity vector and acceleration vector in k direction And as we know from our general concept of projectile matrix in physics that S = 4t + 1/2 at^2 s = 0, as the ball lands mu = 80, as given a = -32, as given So, 0 = 80t - 1/2 times 32 t^2 t (80 - 16t) = 0 \r\n so, the time at which the ball lands it 5 unit So, the y co - ordinate of the port where ball lands, s = mu t + 1/2 at^2 mu = 0, a = -4, t = 5 So, s = 0 (5) + 1/2 (-4) times (5)^2 s = 0 -