Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surface A baseball is hit when it is 2.8 ft above the ground. It leaves the bat with an initial velocity of 149 ft/sec at a launch angle of 24°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of -9.7i (ft/sec) to the ball's initial velocity. Find a vector equation for the path of the baseball.

A minigolf ball is on a perfectly horizontal surface, x = 2 m away from the center of the hole. There is a small obstacle in the way, so the ball cannot simply roll to the hole –it must go up in the air. The player is able to shoot with an initial speed v0 =  7 m/s. The ball can be launched at TWO possible angles with the horizontal for the ball to get in the hole. We want your to find these two angles.

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A batter hits the baseball A with an initial velocity of vo = 91 ft/sec directly toward fielder B at an angle of 38° to the horizontal; the initial position of the ball is 2.4 ft above ground level. Fielder B requires 0.24 sec to judge where the ball should be caught and begins moving to that position with constant speed. Because of great experience, fielder B chooses his running speed so that he arrives at the "catch position" simultaneously with the baseball. The catch position is the field location at which the ball altitude is 7.9 ft. Determine the velocity of the ball relative to the fielder at the instant the catch is made. Vo 438° 2.4' Answer: VA/B = (i 204' B i+ i Next question j) ft/sec

A golfer hits an approach shot with a velocity of 38.2 m/s at 50 degrees above the horizontal. The golf ball lands directly next to the hole, 5.50 m above the ball’s original position, and stops immediately. How far horizontally was the golfer from the hole?

A projectile launcher can launch a projectile with a speed of 38 m/s.  At what angle should a projectile be launched to hit a target at a height 17 m a horizontal distance 20 m away?

A projectile is fired with an initial speed of 36.2 m/s at an angle of 42.3 ° above the horizontal on a long flat firing range.  Determine the maximum height reached by the projectile. Express answer using three significant figures.  Determine the total time in the air. Express answer using three significant figures.  Determine the total horizontal distance covered (that is, the range)  Determine the speed of the projectile 2.00 s after firing.

(a) From a balcony a child fires a toy arrow down to the ground below. The arrow has initial speed 12 m/s and is aimed at an angle of 30° below the horizontal. The arrow takes 1.2 seconds to hit the ground. (i) Calculate the initial horizontal (✰) and vertical (ŷ) velocity components of the arrow. (ii) Calculate the height of the balcony. (b) A projectile is launched with an initial speed of 75 m/s at an angle of 52° above the horizontal. If it lands at the same height from which it was launched, calculate how long the projectile remains in the air.

A projectile is fired with initial speed 150 m/s and an angle of elevation 45° from a position 10 m above ground level. Where does the projectile hit the ground and with what speed? Solution If we place the origin at ground level, then the initial position of the projectile is  (0, 10)  and so we need to adjust the parametric equations of the trajectory by adding 10 to the expression for y. With  v0 = 150 m/s,  ? = 45°, and g = 9.8 m/s2, we have x  =  150 cos    ? 4    t =          y  =  10 + 150 sin    ? 4    t −  1 2  (9.8)t2 =          . Impact occurs when y = 0, that is  4.9t2 − 75   2  t − 10 = 0.  Solving this quadratic equation (and using only the positive value of t), we get the following. (Round your answer to two decimal places.) t =  75   2  +    11,250 + 196 9.8  ≈   Then  x ≈ 75   2 (21.74) ≈    (rounded to the nearest whole number), so the projectile hits the ground about…

A cart is moving with a constant horizontal velocity of 5.00 m/s. A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure) and experiences no significant air resistance. Cart 60° 8.00 m/s -5.00 m/s Just as the pebble returns to the level from which it was launched, what is its distance from the front of the cart? How far did the pebble travel from its launch point relative to the ground.