A. The difference in the two ball's time in the air is 3 seconds
B. The velocity of each ball as it strikes the ground is 24.5 m/s
C. The balls 0.500 s after they are thrown are 14.7 m apart
Further explanation
Acceleration is rate of change of velocity.
\(\large {\boxed {a = \frac{v - u}{t} } }\)
\(\large {\boxed {d = \frac{v + u}{2}~t } }\)
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem!
Given:
Initial Height = H = 19.6 m
Initial Velocity = u = 14.7 m/s
Unknown:
A. Δt = ?
B. v = ?
C. Δh = ?
Solution:
Question A:
First Ball
\(h = H - ut - \frac{1}{2}gt^2\)
\(0 = 19.6 - 14.7t - \frac{1}{2}(9.8)t^2\)
\(0 = 19.6 - 14.7t - 4.9t^2\)
\(4.9t^2 + 14.7t - 19.6 = 0\)
\(t^2 + 3t - 4 = 0\)
\((t + 4)(t - 1) = 0\)
\((t - 1) = 0\)
\(\boxed {t = 1 ~ second}\)
Second Ball
\(h = H + ut - \frac{1}{2}gt^2\)
\(0 = 19.6 + 14.7t - \frac{1}{2}(9.8)t^2\)
\(0 = 19.6 + 14.7t - 4.9t^2\)
\(4.9t^2 - 14.7t - 19.6 = 0\)
\(t^2 - 3t - 4 = 0\)
\((t - 4)(t + 1) = 0\)
\((t - 4) = 0\)
\(\boxed {t = 4 ~ seconds}\)
The difference in the two ball's time in the air is:
\(\Delta t = 4 ~ seconds - 1 ~ second\)
\(\large {\boxed {\Delta t = 3 ~ seconds} }\)
Question B:
First Ball
\(v^2 = u^2 - 2gH\)
\(v^2 = (-14.7)^2 + 2(-9.8)(-19.6)\)
\(v^2 = 600.25\)
\(v = \sqrt {600.25}\)
\(\boxed {v = 24.5 ~ m/s}\)
Second Ball
\(v^2 = u^2 - 2gH\)
\(v^2 = (14.7)^2 + 2(-9.8)(-19.6)\)
\(v^2 = 600.25\)
\(v = \sqrt {600.25}\)
\(\boxed {v = 24.5 ~ m/s}\)
The velocity of each ball as it strikes the ground is 24.5 m/s
Question C:
First Ball
\(h = H - ut - \frac{1}{2}gt^2\)
\(h = 19.6 - 14.7(0.5) - \frac{1}{2}(9.8)(0.5)^2\)
\(\boxed {h = 11.025 ~ m}\)
Second Ball
\(h = H + ut - \frac{1}{2}gt^2\)
\(h = 19.6 + 14.7(0.5) - \frac{1}{2}(9.8)(0.5)^2\)
\(\boxed {h = 25.725 ~ m}\)
The difference in the two ball's height after 0.500 s is:
\(\Delta h = 25.725 ~ m - 11.025 ~ m\)
\(\large {\boxed {\Delta h = 14.7 ~ m} }\)
Learn more
- Velocity of Runner : https://brainly.com/question/3813437
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
Answer details
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle
