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.
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Problem 1: Step 1: Given initial velocity u = 20 m/s upward, g = 10 m/s² downward, find maximum height. Formula for maximum height: h = (u^2)/(2g) Substitute: h = ((20)^2)/(2 × 10) = (400)/(20) = 20 m Final answer: h = 20\ m 20 m Problem 2: Step 1: Car starts from rest, a = 3 m/s², t = 8 s. Find final velocity v. v = u + at = 0 + 3 × 8 = 24 m/s Step 2: Distance s. s = ut + (1)/(2)at^2 = 0 + (1)/(2) × 3 × 64 = 96 m Final answer: v = 24\ m/s, s = 96\ m v = 24 m/s, s = 96 m Problem 3: Step 1: Free fall from rest, t = 4 s, g = 10 m/s². Find velocity and distance. v = gt = 10 × 4 = 40 m/s s = (1)/(2)gt^2 = (1)/(2) × 10 × 16 = 80 m Final answer: v = 40\ m/s, s = 80\ m v = 40 m/s, s = 80 m Problem 4: Step 1: Projectile, u = 30 m/s at 37°, g=10 m/s². Horizontal range. u_x = 30 37^ = 30 × 0.8 = 24 m/s u_y = 30 37^ = 30 × 0.6 = 18 m/s Time of flight: T = (2u_y)/(g) = (2 × 18)/(10) = 3.6 s Range R = u_x T = 24 × 3.6 = 86.4 m Final answer: R = 86.4\ m 86.4 m Problem 5: Step 1: Deceleration a = -4 m/s², initial v=50 m/s, find stopping distance. Use v^2 = u^2 + 2as, v=0 0 = 50^2 + 2(-4)s 200 s = 2500 s = 12.5 m Final answer: s = 12.5\ m 12.5 m