Final answer:
The horizontal displacement of a cannonball launched horizontally from a 179 m cliff at a speed of 26.2 m/s is approximately 158.24 m, calculated by first determining the fall time and then multiplying by the horizontal velocity.
Step-by-step explanation:
To determine the horizontal displacement of a cannonball launched horizontally from the top of a cliff, we need to use the concepts of projectile motion.
In this case, the horizontal motion component is unaffected by gravity and will therefore be at a constant velocity, while the vertical motion component is affected by gravity and will determine the time the cannonball spends in the air.
The horizontal velocity (vx) is given as 26.2 m/s, and the height (h) of the cliff is 179 m. To find out how long it takes for the cannonball to reach the ground, we use the formula for the vertical motion: h = 0.5gt2 where g is the acceleration due to gravity (9.81 m/s2) and t is the time in seconds. After calculating the time t, we then use the horizontal velocity to find the horizontal displacement: x = vxt.
Step-by-step calculation:
- Calculate the time to hit the ground: √(2*179 m / 9.81 m/s2) = √(36.4 s2) = 6.04 s.
- Calculate the horizontal displacement: 26.2 m/s * 6.04 s = 158.24 m.
Therefore, the horizontal displacement of the cannonball would be approximately 158.24 meters.