Answer :
Final answer:
The problem is solved using the principles of projectile motion. The formula δy = 0.5 * g * t^2 is used to calculate the time and then the horizontal initial velocity Vxi = delta x / t to obtain the correct initial velocity, which is option (c) 7.1 m/s. So correct answer is option c.
Explanation:
This is a classic example of a projectile motion problem in physics, where the effects of gravity on a horizontally launched object are analyzed. The problem involves finding the initial velocity of a crossbow bolt that travels a horizontal distance before dropping a certain vertical distance due to gravity. Since the bolt is launched horizontally, its initial vertical velocity is zero, meaning that only gravity influences its vertical motion.
To solve this, we use the formula for the vertical displacement in projectile motion, which is δy = Vyi * t + 0.5 * g * t^2. Since the initial vertical velocity (Vyi) is zero for a horizontally launched projectile, the equation simplifies to δy = 0.5 * g * t^2. Given that the vertical drop (δy) is 0.21 m and the acceleration due to gravity (g) is 9.8 m/s^2, we can solve for the time (t) it takes for the bolt to fall 0.21 m.
Once we have the time, we then use the horizontal distance (delta x) covered, which is 38.1 m, and the formula delta x = Vxi * t, where Vxi is the initial horizontal velocity, to find the initial velocity. Rearranging the formula to solve for Vxi gives us Vxi = delta x / t.
By substituting the calculated time into this formula, we can find that the correct option for the initial velocity of the crossbow bolt is option (c) 7.1 m/s.
