Final answer:
To find the height from which a ball was thrown horizontally, calculate the time for the ball to travel the horizontal distance at a constant speed, and then use this time to find the vertical distance fallen under the influence of gravity.
Step-by-step explanation:
The student's question pertains to projectile motion, specifically calculating the height from which a ball was thrown if it was launched horizontally and traveled a certain distance before hitting the ground. To solve this, we apply the principles of kinematics in two dimensions, separating horizontal and vertical motions since they are independent in projectile motion.
Firstly, we note that the horizontal velocity (30 m/s) remains constant throughout the flight because there is no acceleration in the horizontal direction if we ignore air resistance. The time it takes for the ball to travel the 50 m horizontal distance can be calculated using the formula horizontal distance = horizontal velocity × time.
Once we have the time, we can use it to find the height by applying the equation for the vertical motion: distance fallen = (1/2) × gravity × time2, with gravity being approximately 9.81 m/s2. Knowing that the vertical initial velocity for the horizontal launch is zero, this equation simplifies to determining the vertical distance fallen, which is the height the ball was thrown from.