Question

You throw a snowball horizontally from the roof of a building that is 74.0 m above flat ground. The snowball hits the ground a distance of 45.0 m from the base of the building. Take up to be positive y-direction, and use g = 9.80 m/s2. Take the initial direction of motion of the snowball to be in the positive x-direction. (a) How long does it take for the snowball to hit the ground after you throw it? (b) What is the initial speed of the snowball? (HINT: is this horizontal or vertical?) (c) What is the vertical velocity as it strikes the ground? (would the velocity be positive or negative?) (d) What is the resultant of snowball's speed just before it hits the ground? (HINT: we have a horizontal and a vertical velocity, how can we combine two vectors that are at right angles to each other?)

A) Approximately 3.89 seconds with an initial speed of approximately 11.56 m/s, a vertical velocity of approximately 38.18 m/s, and a resultant speed of approximately 40.11 m/s.
B) Approximately 2.56 seconds with an initial speed of approximately 9.80 m/s, a vertical velocity of 0 m/s, and a resultant speed of approximately 27.28 m/s.
C) Approximately 5.34 seconds with an initial speed of approximately 15.10 m/s, a vertical velocity of approximately 27.28 m/s, and a resultant speed of approximately 38.18 m/s.
D) Approximately 7.21 seconds with an initial speed of approximately 38.18 m/s, a vertical velocity of approximately 38.18 m/s, and a resultant speed of approximately 45.69 m/s.

Answer 1

The snowball's motion in the horizontal and vertical components can be analyzed separately, using the formulas for gravitational acceleration to calculate the time to fall and the velocity components, and the Pythagorean theorem to find the resultant speed.

Step-by-step explanation:

The scenario where a snowball is thrown horizontally from a building and the various aspects of its motion must be analyzed can be broken down into several parts.

(a) Time to Hit the Ground

The time to hit the ground depends only on the vertical motion. The formula for the time 't' taken by an object to fall from a height 'h' under gravity 'g' is derived from h = (1/2)gt2, which simplifies to t = sqrt(2h/g). Substituting h = 74.0 m and g = 9.80 m/s2 into the formula, we can calculate the time taken for the snowball to hit the ground.

(b) Initial Speed of the Snowball

The initial speed in the horizontal direction can be obtained using the horizontal distance and the time from part (a). The formula speed = distance/time is applied here, considering that there's no horizontal acceleration due to gravity.

(c) Vertical Velocity

The vertical velocity at the moment of impact can be calculated by vy = gt. This will be negative since it is directed downwards towards the end of the motion.

(d) Resultant Speed

To find the resultant speed before the snowball hits the ground, we combine the horizontal and vertical components using the Pythagorean theorem due to the right angle formed between the components.