Question

A rock is dropped from a tall building. You can ignore air resistance. Determine its final speed and distance traveled after 4 seconds.

(A) speed = 20 m/s, distance = 80 m
(B) speed = 40 m/s, distance = 20 m
(C) speed = 40 m/s, distance = 80 m
(D) speed = 80 m/s, distance = 40 m
(E) speed = 20 m/s, distance = 40 m ​

Answer 1

Using kinematic equations, the final speed for a rock dropped from a tall building and ignoring air resistance after 4 seconds is 40 m/s, and the distance traveled is 80 m. The correct answer is (C).

Step-by-step explanation:

To determine the final speed and distance traveled after 4 seconds for a rock dropped from a tall building with no air resistance, we can use kinematic equations. The acceleration due to gravity (g) is 9.8 m/s². The initial velocity (u) is 0 m/s since the rock is simply dropped.

The final velocity (v) after time (t) is given by:
v = u + gt
v = 0 + (9.8 m/s²)(4 s)
v = 39.2 m/s
To the nearest whole number, the final speed will be 40 m/s.

The distance (s) traveled is given by:
s = ut + \(\frac{1}{2}\)gt²
s = 0 + \(\frac{1}{2}\)(9.8 m/s²)(4 s)²
s = 78.4 m
To the nearest whole number, the distance traveled will be 80 m.

Therefore, the correct answer is (C) speed = 40 m/s, distance = 80 m.

Answer 2

(C) speed = 40 m/s, distance = 80 m

Step-by-step explanation:

According to Newton law of motion for a falling body:

v = u + gt

Where v is the final velocity, u is the initial velocity, t is the time taken to fall and g is the acceleration due to gravity.

Given that: t = 4 s, g = 10 m/s², u = 0 m/s(at top of building). Therefore substituting values:

v = 0 + 10(4)

v = 40 m/s

To find the distance h, we use the formula:

v² = u² + 2gh

Substituting values:

40² = 0² + 2(10)h

20h = 40² - 0²

20h = 1600

h = 1600 / 20

h = 80 m

The speed = 40 m/s, distance = 80 m