v = 60m/s
initial height = 210m
x = v(t)
t = x/v
y = (g)(t²)/2
y = (g)(x/v)²/2
y = (g)(x²)/(2)(v²)
y = (9.81)(x²/(2)(60²)
210 = 9.81(x²)/2(3600)
210 = 9.81(x²)/7200
210(7200) = 9.81x²
1,512,000/9.81 = x²
x = √154,128.44
x = 392.6m
h = g(t²)/2
2h = gt²
t = √(2h/g)
t = √2(210)/(9.81)
t = √(420/9.81)
t = √42.81
t = 6.54sec
v = 59m/s
initial height = 165m
t = √2(165)/(9.81)
t = √(330/9.81)
t = √33.6391
t = 5.79sec
y = (9.81)(x²/(2)(59²)
165 = 9.81(x²)/2(3481)
165 = 9.81(x²)/6962
165(6962) = 9.81x²
1,148,730/9.81 = x²
x = √117,097.859
x = 342.1956m
Initial velocity = 37 m/s
angle = 55 degrees
initial height = 0
Vy = vsinα
Vy = 37sin55
Vy = 30.3086256387
t = 2(Vy)/g
t = 2(30.3086256387)/9.81
t = 6.179sec
Vx = vcosα
Vx = 37cos55
Vx = 21.222328145
range = 2(Vx)(Vy)/g
range = 2(21.222328145)(30.3086256387)/9.81
range = 131.135m
Max height = (Vy)²/2g
Max height = (30.3086256387)²/2(9.81)
Max height = 918.61278810686298293769/19.62
Max height = 46.82m
Initial velocity = 38 m/s
angle = 56 degrees
Vy = 38sin56
Vy = 31.5034277571
t = 2(31.5034277571)/9.81
t = 6.42sec
Vx = 38cos56
Vx = 21.2493303319
range = 2(21.2493303319)(31.5034277571)/9.81
range = 136.478m
Max height = (31.5034277571)²/2(9.81)
Max height = 992.46596044681873660041/19.62
Max height = 50.58m
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Answers & Comments
Problem 1:
Given:
v = 60m/s
initial height = 210m
Solution:
a.)
x = v(t)
t = x/v
y = (g)(t²)/2
y = (g)(x/v)²/2
y = (g)(x²)/(2)(v²)
y = (9.81)(x²/(2)(60²)
210 = 9.81(x²)/2(3600)
210 = 9.81(x²)/7200
210(7200) = 9.81x²
1,512,000/9.81 = x²
x = √154,128.44
x = 392.6m
b.)
h = g(t²)/2
2h = gt²
t = √(2h/g)
t = √2(210)/(9.81)
t = √(420/9.81)
t = √42.81
t = 6.54sec
Problem 2:
Given:
v = 59m/s
initial height = 165m
Solution:
a.)
h = g(t²)/2
2h = gt²
t = √(2h/g)
t = √2(165)/(9.81)
t = √(330/9.81)
t = √33.6391
t = 5.79sec
b.)
x = v(t)
t = x/v
y = (g)(t²)/2
y = (g)(x/v)²/2
y = (g)(x²)/(2)(v²)
y = (9.81)(x²/(2)(59²)
165 = 9.81(x²)/2(3481)
165 = 9.81(x²)/6962
165(6962) = 9.81x²
1,148,730/9.81 = x²
x = √117,097.859
x = 342.1956m
Problem 3:
Given:
Initial velocity = 37 m/s
angle = 55 degrees
initial height = 0
Solution:
Vy = vsinα
Vy = 37sin55
Vy = 30.3086256387
a.)
t = 2(Vy)/g
t = 2(30.3086256387)/9.81
t = 6.179sec
b.)
Vx = vcosα
Vx = 37cos55
Vx = 21.222328145
range = 2(Vx)(Vy)/g
range = 2(21.222328145)(30.3086256387)/9.81
range = 131.135m
c.)
Max height = (Vy)²/2g
Max height = (30.3086256387)²/2(9.81)
Max height = 918.61278810686298293769/19.62
Max height = 46.82m
Problem 4:
Given:
Initial velocity = 38 m/s
angle = 56 degrees
initial height = 0
Solution:
Vy = vsinα
Vy = 38sin56
Vy = 31.5034277571
a.)
t = 2(Vy)/g
t = 2(31.5034277571)/9.81
t = 6.42sec
b.)
Vx = vcosα
Vx = 38cos56
Vx = 21.2493303319
range = 2(Vx)(Vy)/g
range = 2(21.2493303319)(31.5034277571)/9.81
range = 136.478m
c.)
Max height = (Vy)²/2g
Max height = (31.5034277571)²/2(9.81)
Max height = 992.46596044681873660041/19.62
Max height = 50.58m
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