This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the breakdown of the problem: Given: Distance to goal post, x = 40.0 m Height of goal post, h_goal = 2.2 m Initial velocity, v_0 = 40 m/s Launch angle, = 10^ Acceleration due to gravity, g = 9.8 m/s^2 (assumed) a) Show by calculation whether she hits the target or not. Step 1: Resolve the initial velocity into horizontal and vertical components. v_0x = v_0 = 40 (10^) m/s v_0y = v_0 = 40 (10^) m/s Using a calculator: v_0x ≈ 40 × 0.9848 = 39.392 m/s v_0y ≈ 40 × 0.1736 = 6.944 m/s Step 2: Calculate the time (t) it takes for the ball to reach the horizontal distance of the goal post. The horizontal motion is uniform (constant velocity). x = v_0x t 40.0 m = (39.392 m/s) t t = (40.0)/(39.392) s t ≈ 1.0154 s Step 3: Calculate the vertical height (y) of the ball at this time t. The vertical motion is uniformly accelerated. y = v_0y t - (1)/(2)gt^2 y = (6.944 m/s)(1.0154 s) - (1)/(2)(9.8 m/s^2)(1.0154 s)^2 y = 7.050 m - (4.9 m/s^2)(1.0310 s^2) y = 7.050 m - 5.052 m y = 1.998 m Step 4: Compare the calculated height with the goal post height. The height of the ball when it reaches the goal post is 1.998 m. The height of the goal post is 2.2 m. Since 1.998 m < 2.2 m, the ball passes under the crossbar. It is also above the ground (0 m). Therefore, the ball hits the target (the goal area). The ball hits the target. b) Explain why the ball is parabolic. The trajectory of the ball is parabolic because it undergoes two independent motions simultaneously: • Horizontal motion: The ball moves with a constant velocity in the horizontal direction (assuming no air resistance). • Vertical motion: The ball experiences a constant downward acceleration due to gravity. The combination of these two motions—one uniform and one uniformly accelerated—results in a path that is a segment of a parabola. Last free one today — make it count tomorrow, or type /upgrade for unlimited.