Answer:
Ball hit the tall building 50 m away below 10.20 m its original level
Explanation:
Horizontal speed = 20 cos40 = 15.32 m/s
Horizontal displacement = 50 m
Horizontal acceleration = 0 m/s²
Substituting in s = ut + 0.5at²
50 = 15.32 t + 0.5 x 0 x t²
t = 3.26 s
Now we need to find how much vertical distance ball travels in 3.26 s.
Initial vertical speed = 20 sin40 = 12.86 m/s
Time = 3.26 s
Vertical acceleration = -9.81 m/s²
Substituting in s = ut + 0.5at²
s = 12.86 x 3.26 + 0.5 x -9.81 x 3.26²
s = -10.20 m
So ball hit the tall building 50 m away below 10.20 m its original level
Answer:
Vmax=11.53 m/s
Explanation:
from conservation of energy

Spring potential energy =potential energy due to elevation
0.5*k*x²= mg
=mgh
0.5*k*2.3²= 430*9.81*6
k=9568.92 N/m
For safety reason
k"=1.13 *k= 1.13*9568.92
k"=10812.88 N/m
agsin from conservation of energy

spring potential energy=change in kinetic energy
0.5*k"*x²=0.5*m*
10812.88 *2.3²=430*
=11.53 m/s
Answer:
M[min] = M[basket+people+ balloon, not gas] * ΔR/R[b]
ΔR is the difference in density between the gas inside and surrounding the balloon.
R[b] is the density of gas inside the baloon.
====================================
Let V be the volume of helium required.
Upthrust on helium = Weight of the volume of air displaced = Density of air * g * Volume of helium = 1.225 * g * V
U = 1.225gV newtons
----
Weight of Helium = Volume of Helium * Density of Helium * g
W[h] = 0.18gV N
Net Upward force produced by helium, F = Upthrust - Weight = (1.225-0.18) gV = 1.045gV N -----
Weight of 260kg = 2549.7 N
Then to lift the whole thing, F > 2549.7
So minimal F would be 2549.7
----
1.045gV = 2549.7
V = 248.8 m^3
Mass of helium required = V * Density of Helium = 248.8 * 0.18 = 44.8kg (3sf)
=====
Let the density of the surroundings be R
Then U-W = (1-0.9)RgV = 0.1RgV
So 0.1RgV = 2549.7 N
V = 2549.7 / 0.1Rg
Assuming that R is again 1.255, V = 2071.7 m^3
Then mass of hot air required = 230.2 * 0.9R = 2340 kg
Notice from this that M = 2549.7/0.9Rg * 0.1R so
M[min] = Weight of basket * (difference in density between balloon's gas and surroundings / density of gas in balloon)
M[min] = M[basket] * ΔR/R[b]
As we know that gravitational potential energy is given by

here we have
m = mass = 120 kg

h = height = 8.2 m
now from above formula


so above is the gravitational potential energy of the couch
Answer:
the average force exerted on the ball by the bat is 11,613.27 N
Explanation:
Given;
mass of the baseball, m = 151 g = 0.151 kg
initial velocity of the baseball, u = 39.5 m/s
final velocity of the baseball, v = 45.1 m/s
time of action, t = 1.10 ms = 1.10 x 10⁻³ s
The average force exerted on the ball by the bat is calculate as;
Therefore, the average force exerted on the ball by the bat is 11,613.27 N