Answer:
Ai. Speed of the fragment with mass mA= 1.35 kg is 34.64 m/s
Aii. Speed of the fragment with mass mB = 0.270 kg is 77.46 m/s
B. 475.3 m
Explanation:
A. Determination of the speed of each fragment.
I. Determination of the speed of the fragment with mass mA = 1.35 kg
Mass of fragment (m₁) = 1.35 kg
Kinetic energy (KE) = 810 J
Velocity of fragment (u₁) =?
KE = ½m₁u₁²
810 = ½ × 1.35 × u₁²
810 = 0.675 × u₁²
Divide both side by 0.675
u₁² = 810 / 0.675
u₁² = 1200
Take the square root of both side.
u₁ = √1200
u₁ = 34.64 m/s
Therefore, the speed of the fragment with mass mA = 1.35 kg is 34.64 m/s
II. I. Determination of the speed of the fragment with mass mB = 0.270 kg
Mass of fragment (m₂) = 0.270 kg
Kinetic energy (KE) = 810 J
Velocity of fragment (u₂) =?
KE = ½m₂u₂²
810 = ½ × 0.270 × u₂²
810 = 0.135 × u₂²
Divide both side by 0.135
u₂² = 810 / 0.135
u₂² = 6000
Take the square root of both side.
u₂ = √6000
u₂ = 77.46 m/s
Therefore, the speed of the fragment with mass mB = 0.270 kg is 77.46 m/s
B. Determination of the distance between the points on the ground where they land.
We'll begin by calculating the time taken for the fragments to get to the ground. This can be obtained as follow:
Maximum height (h) = 90.0 m
Acceleration due to gravity (g) = 10 m/s²
Time (t) =?
h = ½gt²
90 = ½ × 10 × t²
90 = 5 × t²
Divide both side by 5
t² = 90/5
t² = 18
Take the square root of both side
t = √18
t = 4.24 s
Thus, it will take 4.24 s for each fragments to get to the ground.
Next, we shall determine the horizontal distance travelled by the fragment with mass mA = 1.35 kg. This is illustrated below:
Velocity of fragment (u₁) = 34.64 m/s
Time (t) = 4.24 s
Horizontal distance travelled by the fragment (s₁) =?
s₁ = u₁t
s₁ = 34.64 × 4.24
s₁ = 146.87 m
Next, we shall determine the horizontal distance travelled by the fragment with mass mB = 0.270 kg. This is illustrated below:
Velocity of fragment (u₂) = 77.46 m/s
Time (t) = 4.24 s
Horizontal distance travelled by the fragment (s₂) =?
s₂ = u₂t
s₂ = 77.46 × 4.24
s₂ = 328.43 m
Finally, we shall determine the distance between the points on the ground where they land.
Horizontal distance travelled by the 1st fragment (s₁) = 146.87 m
Horizontal distance travelled by the 2nd fragment (s₂) = 328.43 m
Distance apart (S) =?
S = s₁ + s₂
S = 146.87 + 328.43
S = 475.3 m
Therefore, the distance between the points on the ground where they land is 475.3 m
