Q1. The answer is 1.32 s.
The kinetic equation used to calculate the time is:
d = v1 t + 1/2 at²
d - distance
v1 - initial velocity
t - time
a - gravitational acceleration
We know:
d = - 8.52 m (negative because it is downwards)
v1 = 0 (there is no initial velocity in free fall)
a = - 9.8 m/s² (negative in free falls)
d = v1 t + 1/2 at²
- 8.52 = 0 * t + 1/2 * - 9.8 * t²
- 8.52 = 0 - 4.9 t²
-8.52 = -4.9 t²
t² = -8.52/-4.9
t² = 1.74
t = √1.74
t = 1.32 s
Q2. PART A) The answer is 35 m.
The kinetic equation that can be used is:
v2² = v1² +2ad
d - distance
v1 - initial velocity
v2 - final velocity
a - gravitational acceleration
We know:
v2 = 0 (The final velocity is at the peak so it is 0)
v1 = 26.2 m/s
a = 9.8 m/s² (negative in free falls)
d = ?
v2² = v1² +2ad
0 = 26.2² + 2 * ( - 9.8) * d
0 = 686.44 - 19.6d
19.6d = 686.44
d = 686.44/19.6
d = 35.0 m
Q2. PART B) The answer is 26.2 m/s.
The velocity at what is the vase moving when Rex catches is v2.
It is free fall from the height calculated in part A.
The kinetic equation that can be used is:
v2² = v1² + 2*a*d
v1 - initial velocityv2 - final velocitya - gravitational accelerationd - distance
We know:v2 = ?v1 = 0 (in free fall)a = - 9.8 m/s² (negative in free falls)d = - 35 m (negative because it is downwards)
v2² = v1² + 2*a*d
v2² = 0 + 2 * -9.8 * -35
v2² = 686v2 = √686v2 = 26.2 m/s
Q3. PART A) The answer is -147 m/s
The kinetic equation that can be used is:v2 = v1 + a * tv1 - initial velocityv2 - final velocitya - gravitational accelerationt - time
We know:v1 = 0 (the initial speed is 0 at free fall)v2 = ?a = - 9.8 m/s² (negative in free fall)t = 15s
v2 = v1 + a * t
v2 = 0 + -9.8 * 15v2 = -147 m/s
Q3. PART B) The answer is 1102.5 m.
The kinetic equation that can be used is:v2² = v1² +2add - displacementv1 - initial velocityv2 - final velocitya - gravitational acceleration
We know:v2 = -147 m/sv1 = 0 (in free fall)a = -9.8 m/s² (negative in free falls)
v2² = v1² +2ad
-147² = 0 + 2 * -9.8 * d
21609 = -19.6d
d = 21609 / -19.6
d = - 1102.5 m
Displacement is negative, but the height cannot be negative so it is 1102.5m
Q4. PART A) The answer is -13.3 m/s
The kinetic equation that can be used is:v2 = v1 + a * tv1 - initial velocityv2 - final velocitya - gravitational accelerationt - time
We know:v2 = ?v1 = 21 m/sa = 9.8 m/s (negative in free fall)t = 3.5s
v2 = v1 + a * t
v2 = 21 + (-9.8)*3.5v2 = 21 - 34.3v2 = -13.3 m/s
Q4. PART B) The answer is 9.025 m
The kinetic equation that can be used is:v2² = v1² +2add - displacementv1 - initial velocityv2 - final velocitya - gravitational acceleration
We know:
v2 = -13.3 m/s
v1 = 0 (in free fall)
a = -9.8 m/s (in free fall)
v2² = v1² +2ad
-13.3² = 0 + 2 * -9.8 * d
176.89 = 0 - 19.6 * d
176.89 = -19.6 * d
d = 176.89 / -19.6
d = - 9.025 m
Displacement is negative, but the height cannot be negative so it is 9.025 m
Q4. PART C) The answer is the orange is travelling down.
According to the part B of the question, displacement is negative value. The negative value of the displacement is when object goes downwards, thus, it travels down.
Q5. PART A) The answer is 24.7 m
v2² = v1² +2add - displacementv1 - initial velocityv2 - final velocitya - gravitational acceleration
We know:v2 = 0 (when it reaches the ground)v1 = 22 m/st = 6.4 sa = -9.8 m/s (in free fall)
v2² = v1² +2ad
0 = 22² + 2 * -9.8 * d
0 = 484 + -19.6d
-484 = - 19.6d
d = -484/-19.6
d = 24.7 m
PART B) The answer is 2.24m
The kinetic equation used to calculate the time is:v2 = v1 + a*hh - heightv1 - initial velocityv2 - final velocitya - gravitational acceleration
We know:v1 = 22 m/sv2 = 0h = ?a = -9.8 m/s (negative in free fall)
v2 = v1 + a*h
0 = 22 + -9.8 * h-22 = -9.8hh = -22/-9.8h = 2.24 m