Projectile Motion

Answer (d)

Answer (a) 1.55 sec

Step 1: Understanding projectile motion The range of a projectile launched at an angle is given by: The maximum range occurs when the projectile is launched at or : Given that the maximum range is 80 m, we set: Step 2: Finding the range at For an angle , the range is: Substituting : Since: Step 3: Verifying the correct option Comparing with given options, the correct answer is:

Let the initial velocity be and the height be . The ball is projected upwards, and it reaches the ground with a speed of . We can use the equation of motion for vertical displacement and velocity. The equation relating velocity, acceleration, and displacement is: where: - is the final velocity, - is the initial velocity, - is the acceleration (which is , the acceleration due to gravity, as the ball is moving upwards), - is the displacement (which in this case is ). At the point when the ball reaches the ground, we have: - Final velocity , - Initial velocity , - Displacement , - Acceleration . Using the equation: Simplifying: Thus, the height is . Now, we need to find the time taken by the ball to reach the ground. The time can be found from the equation: Using the same values for , , and , we get: Solving for : Thus, the time taken by the ball to reach the ground is . So, the correct answer is (B) , .