Final answer:
To find how far from the base of the cliff the ball will land, calculate the fall time using the formula t = sqrt(2h/g) and then use this time to determine the horizontal distance with d = v_x * t using the initial horizontal velocity of 16.0 m/s.
Step-by-step explanation:
To determine how far from the base of the cliff the ball will strike the ground, we need to calculate the time it takes for the ball to fall 150 m vertically and then use this time to find out how far it will travel horizontally at a constant speed of 16.0 m/s. The vertical motion is governed by the equations of motion for freely falling objects under gravity, assuming no air resistance.
Step 1: Calculate the time of fall
The formula for the time t it takes an object to fall from a height h under gravity g is derived from s = 1/2gt2, where s is the distance fallen and g is the acceleration due to gravity (approximately 9.81 m/s2). We rearrange the formula to solve for t: t = sqrt(2h/g). For a height of 150 m, t = sqrt(2*150/9.81), which gives us the time of fall.
Step 2: Determine horizontal distance
While the ball is falling, it also travels horizontally. Since there is no acceleration horizontally, the horizontal distance d can be found using the formula d = vx * t, where vx is the horizontal velocity. With the time from step 1 and the given speed of 16.0 m/s, the horizontal distance can be calculated.
After performing the calculations, we find that the ball will strike the ground at a distance determined by these steps from the base of the cliff.