A water balloon is thrown into the air and lands 30.0 meters away 1.8 seconds later.
a. What was the speed of the balloon thrown (on the diagonal)
b. At what angle was the balloon thrown with respect to the ground?
D = Xo * 1.8 = 30 m.
Xo = 30/1.8 = 16.67 m/s=Hor. component of initial velocity.
Y = Yo + g*Tr = 0 at max Ht.
Yo - 9.8*(1.8/2) = 0
Yo - 8.82 = 0
Yo = 8.82 m/s = Ver. component of initial velocity.
a. Vo^2=Xo^2 + Yo^2=16.67^2 + 8.82^2 =
355.7
Vo = 18.9 m/s = Initial velocity.
b. tan A = Yo/Xo = 8.82/16.67 = 0.52909
A = 27.9o
To solve this problem, we can use the equations of motion to find the speed and angle at which the water balloon was thrown.
a. First, let's find the vertical component of the velocity (V_y) of the balloon when it lands. We will use the equation:
V_y = V_initial * sin(theta)
where V_initial is the initial velocity of the balloon and theta is the angle at which it was thrown.
Since we are given the vertical distance (y = 0) and the time of flight (t = 1.8 s), we can use the equation:
y = V_y * t - (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the values, we get:
0 = V_y * 1.8 - (1/2) * 9.8 * (1.8)^2
Solving this equation will give us the value of V_y.
Next, let's find the horizontal component of the velocity (V_x). We will use the equation:
V_x = V_initial * cos(theta)
Since the horizontal distance (x) is given as 30.0 meters and the time of flight is 1.8 seconds, we have:
x = V_x * t
Substituting the values, we get:
30.0 = V_x * 1.8
Solving this equation will give us the value of V_x.
Finally, we can find the total velocity (V) of the balloon using the Pythagorean theorem:
V = sqrt(V_x^2 + V_y^2)
This will give us the speed of the balloon thrown on the diagonal.
b. To find the angle at which the balloon was thrown with respect to the ground, we can use the equation:
tan(theta) = V_y / V_x
We already have the values of V_y and V_x, so we can calculate the tangent of the angle and then use the inverse tangent function to find the angle itself.
By following these steps, you can find the speed and angle at which the water balloon was thrown.