Answer:
We are given the trajectory of a projectile:
y=H+xtan(θ)−g2u2x2(1+tan2(θ)),
where H is the initial height, g is the (positive) gravitational constant and u is the initial speed. Since we are looking for the maximum range we set y=0 (i.e. the projectile is on the ground). If we let L=u2/g, then
H+xtan(θ)−12Lx2(1+tan2(θ))=0
Differentiate both sides with respect to θ.
dxdθtan(θ)+xsec2(θ)−[1Lxdxdθ(1+tan2(θ))+12Lx2(2tan(θ)sec2(θ))]=0
Solving for dxdθ yields
dxdθ=xsec2(θ)[xLtan(θ)−1]tan(θ)−xL(1+tan2(θ))
This derivative is 0 when tan(θ)=Lx and hence this corresponds to a critical number θ for the range of the projectile. We should now show that the x value it corresponds to is a maximum, but I'll just assume that's the case. It pretty obvious in the setting of the problem. Finally, we replace tan(θ) with Lx in the second equation from the top and solve for x.
H+L−12Lx2−L2=0.
This leads immediately to x=L2+2LH−−−−−−−−√. The angle θ can now be found easily.
Answer:
i don't know but have a good day
Complete Question:
Football player A has a mass of 110 kg, and he is running down the field with a velocity of 2 m/s. Football player B has a mass of 120 kg and is stationary. What is the total momentum after the collision?
Answer:
Total momentum = 220 Kgm/s.
Explanation:
<u>Given the following data;</u>
For footballer A
Mass, M1 = 110kg
Velocity, V1 = 2m/s
For footballer B
Mass, M1 = 120kg
Velocity, V1 = 0m/s since he's stationary.
To find the total momentum;
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
a. To find the momentum of A;
Momentum A = 220 Kgm/s.
b. To find the momentum of B;
Momentum B = 0 Kgm/s.
c. To find the total momentum of the two persons;
Substituting into the equation, we have;
<em>Total momentum = 220 Kgm/s. </em>
Newton's 2nd law of motion:
Force = (mass) x (acceleration)
Divide each side by (mass):
Acceleration = (force) / (mass)
= (100 N) / (50 kg)
= 2 m/s²