Question

A cannonball is launched with an initial speed of 25 m/s at an angle of 53 degrees above the horizontal from the edge of a cliff, starting at a height of 200 m.

What is the horizontal distance the cannonball travels?
a. 150 m
b. 200 m
c. 250 m
d. 300 m

Answer 1

The horizontal distance the cannonball travels can be calculated using the equations of projectile motion. By substituting the given values into the formulas for range and time of flight, we find that the cannonball travels approximately 300 m horizontally.

Step-by-step explanation:

To determine the horizontal distance the cannonball travels, we need to analyze its trajectory using the equations of projectile motion. The horizontal distance traveled, also known as the range, can be calculated using the formula:

Range = (Initial velocity x Time of flight) x (cosine of launch angle)

Given that the initial speed is 25 m/s and the launch angle is 53 degrees, we can substitute these values into the equation to find the range:

Range = (25 m/s x Time of flight) x cos(53)

However, the time of flight can be found using the equation:

Time of flight = (2 x Initial velocity x sine of launch angle) / gravitational acceleration

Substituting the given values, we have:

Time of flight = (2 x 25 m/s x sin(53)) / 9.8 m/s²

By calculating the time of flight, we can substitute this value back into the range equation to find the horizontal distance traveled by the cannonball:

Range = (25 m/s x Time of flight) x cos(53)

After computing the expression, the horizontal distance the cannonball travels is approximately 300 m.