A ball thrown horizontally at 22.2 m/s from the roof of a building lands 36.0 m from the base of the building. how high is the b
uilding?
1 answer:
Refer to the diagram shown below.
h = the height of the building
g = 9.8 m/s²
Wind resistance is ignored.
u = 22.2 m/s, horizontal velocity.
The initial vertical velocity is zero.
The time of flight, t, obeys the equation
h = (1/2)*g*t²
That is,
h = 0.5*(9.8 m/s²)*(t s)² = 4.9t²
Because the horizontal distance traveled is 36.0 m, therefore
(22.2 m/s)*(0.4518√h) = 36.0
10.03√h = 36
√h = 3.5892
h = 12.882 m
Answer: 12.9 m (nearest tenth)
h = the height of the building
g = 9.8 m/s²
Wind resistance is ignored.
u = 22.2 m/s, horizontal velocity.
The initial vertical velocity is zero.
The time of flight, t, obeys the equation
h = (1/2)*g*t²
That is,
h = 0.5*(9.8 m/s²)*(t s)² = 4.9t²
Because the horizontal distance traveled is 36.0 m, therefore
(22.2 m/s)*(0.4518√h) = 36.0
10.03√h = 36
√h = 3.5892
h = 12.882 m
Answer: 12.9 m (nearest tenth)
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Answer:
The BMX lands 5.4 m from the end of the ramp.
Explanation:
Hi there!
The position of the BMX is given by the position vector "r":
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
Where:
r = position vector at time t
x0 = initial horizontal position
v0 = initial velocity
α = jumping angle
y0 = initial vertical position
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)
Please, see the attached graphic for a better understanding of the situation. At final time, when the bicycle reaches the ground, the vector position will be "r final" (see figure). The y-component of the vector "r final" is - 2.4 m (placing the origin of the frame of reference at the jumping point). With that information, we can use the equation of the y-component of the vector "r" (see above) to calculate the time of flight. With that time, we can then obtain the x-component (rx in the figure) of the vector "r final". Then:
y = y0 + v0 · t · sin α + 1/2 · g · t²
-2.4 m = 0 m + 5.9 m/s · t · sin 40° - 1/2 · 9.8 m/s² · t²
0 = -4.9 m/s² · t² + 5.9 m/s · t · sin 40° + 2.4 m
Solving the quadratic equation:
t = 1.2 s
Now, we can calculate the x-component of the vector "r final" that is the horizontal distance traveled by the bicycle:
x = x0 + v0 · t · cos α
x = 0 m + 5.9 m/s · 1.2 s · cos 40°
x = 5.4 m
The BMX lands 5.4 m from the end of the ramp.
Have a nice day!
Answer:
Length of third side = 3.97m
Explanation:
First of all, let we draw the triangle from the given information assuming our first corner is A. second corner is B and third corner is C.
From A-B we have distance = 5.5m = Say it c
From B-C we have distance = 4.3m = Say it a
From A-C we have distance = ? = Say it b which we have to find out.
Using the Law of Cosines: The square of the unknown side equals to the sum of squares of other 2 sides and subtracting 2*(Product of other sides)*(Cos(Angle opposite to the unknown side)
For our case it is:
b² = a² + c² - 2acCos(B) - Say it equation 1
From the attached triangle you may see that, a & c are our known sides and B is the angle opposite to the side b.
There values are:
a = 4.3m; c = 5.5m ; Angle B = 0.8 rad = 0.8 * 57.3 = 45.84 degrees where 1 rad = 57.3 degrees
Now by putting the respectve values in equation 1 we have:
b² = (4.3)² + (5.5)² - 2*4.3*5.5*Cos(45.84)
b² = 18.49 + 30.25 - 32.95
b² = 15.79
b = √15.79
b = 3.97m
Thus the length of third side is 3.97m.
PS: The picture of triangle is being attached for yours understanding.
