Hello, I need help with these general physics problems. I have the answers writt

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Hello, I need help with these general physics problems. I have the answers written down, but I need to know how to get to that answer. If you can show work step by step on how to get the answer I have that would be awesome, please, and thank you. I will rate 5 stars for whoever can just show me how to solve the problem(s)!

1.) The minimum takeoff speed for a certain airplane is 75 m/s. What minimum acceleration is required if the plane must take off from a runway of length 950m? Assume the plane starts from rest at one end of the runway. ANSWER: 3.0m/s^2

2.) A ball is dropped from the top of a tall building. At the same instant, a person is running on the ground at a velocity of 4.6 m/s towards the building. If the person was 18m from the building when the ball was dropped and just makes it to the building in time to catch it, how tall is the building? (You can ignore the height of the person and assume that the ball is caught at ground level. ) ANSWER: 75m

3.) Two forces act on a 10-kg mass. One force has a magnitude of 40 N and pushes the mass in the positive-x direction. The second force has a magnitude of 60N and is directed at an angle of 45 degrees above the positive-x axis. What is the magnitude and direction of the acceleration of the mass? ANSWER: 9.3 m/s^2 and 27 degrees above the positive x-axis

4.) Two ice skaters, Paula and Tom, are each holding on to opposite ends of the same rope. They both pull on the rope and move toward each other. The magnitude of Paula's acceleration is 1.25 times greater than the magnitude of Tom's acceleration. What is the ration of Paula's mass to Tom's mass? ANSWER: 0.80

A plane is headed eastward at a speed of 156m/s. A 20.0 m/s wind is blowing southward at thesame time as the plane is flying. The velocity of the plane relative to the ground is. ANSWER: 157 m/s at an angle 7.31 degrees south of east

Explanation / Answer

1) by newtons law of motion

v^2 - u^2 = 2a*s

75^2 - 0 = 2*a*950

a = 2.96 m/s^2

2)time taken by man = 18/4.6 = 3.91 s

and for ball u = 0

a = 9.8

t = 3.91

so

S = ut+at^2/2

S = 0 + 9.8^3.91^2/2

S = 75 m

3) net acc in +ve x dir

F = 40 + 60cos45 = .71.52

a = 71.52/10 = 7.15

acc in -y dir = 60sin45/10 = 5.1

so net acc = sqrt(7.15^2 + 5.1^2) =

and dir = taninvers(7.15/5.1) =

4) here force is same

so m1*a1 = m2*a2

m1*1.25 = m2

m1 = 0.8m2

5) velocity = sqrt(156^2 + 20^2) = 157

angle = tan inverse(20/156) =

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