Calculate the horizontal component of the velocity. The horizontal component of the velocity is given by:
v_x = v * cos(theta)
where v is the original speed of the arrow and theta is the angle of projection.In this case, v = 2 m/s and theta is unknown. Solving for theta, we get:
theta = arccos(v_x / v)
theta = arccos(2 / 2) = 45 degrees
Calculate the vertical component of the velocity. The vertical component of the velocity is given by:
v_y = v * sin(theta)
In this case, v = 2 m/s and theta = 45 degrees. Solving for v_y, we get:
v_y = 2 * sin(45 degrees) = 1.414 m/s
Calculate the time of flight. The time of flight is given by:
t = 2 * v_y / g
In this case, v_y = 1.414 m/s and g = 10 m/s^2. Solving for t, we get:
t = 2 * 1.414 / 10 = 0.283 seconds
Calculate the height of the arrow. The height of the arrow is given by:
y = v_y * t - 0.5 * g * t^2
In this case, v_y = 1.414 m/s, t = 0.283 seconds, and g = 10 m/s^2. Solving for y, we get:
y = 1.414 * 0.283 - 0.5 * 10 * 0.283^2 = 0.303 meters
Therefore, the angle of projection is 45 degrees and the height of the arrow is 0.303 meters.