A bowling ball is rolled down the alley with a constant with a constant velocity of 1.5 m/sec. at an angle of 87 degrees to the starting line. The position of the person throwing the bowling ball can be represented by the point (0,0). Where is the ball after 7 seconds?
A. (0.5, 10.5)
B. (0.1, 1.5)
C. (10.5, 10.5)
D. (29, 200)
Assuming down the alley toward the pins is the +y direction, then
(x,y) = 7*1.5 * (cos87,sin87)
Use the equations x(t)=v(cos theta t)+x1 and y(t)=v(sin theta t)+y1.
First x(t):
(1.5cos87°t)+0= x(t)=0.079t+0
Second y(t):
(1.5sin87°t)+0= y(t)=1.5t+0
Since it's 7 seconds, plug 7 into t:
x(t)=0.079(7)+0 which is 0.5
y(t)=1.5(7)+0 which is 10.5
Hence, the answer is A (0.5,10.5).
oobleck when I solves the equation you presented, I got 10.5 (0.052, 0.99). What does that mean?
To find the position of the ball after 7 seconds, we need to break down the initial velocity into its horizontal and vertical components.
The initial velocity is 1.5 m/s at an angle of 87 degrees with respect to the starting line. Let's call the horizontal component of the velocity Vx and the vertical component Vy.
Vx = V * cos(theta) = 1.5 * cos(87)
Vy = V * sin(theta) = 1.5 * sin(87)
Next, we can calculate the horizontal and vertical displacements (dx and dy) by using the following equations of motion:
dx = Vx * t
dy = Vy * t + (1/2) * g * t^2
Where t is the time in seconds and g is the acceleration due to gravity (approximately 9.8 m/s^2).
dx = Vx * t = (1.5 * cos(87)) * 7
dy = Vy * t + (1/2) * g * t^2 = (1.5 * sin(87)) * 7 + (0.5) * (9.8) * (7^2)
After evaluating these equations, we can find the position of the ball by adding the displacements to the initial position (0,0).
So, the position of the ball after 7 seconds is approximately (0.5, 10.5), which matches option A.