A 1kg mass is launched from the ground into the air at an angle of 30 degrees to the horizontal and with initial speed 25 ms^-1. Assuming negligible air resistance, how far from the starting point will the mass travel before it hits the ground?
1: Draw a diagram2: Split the velocity into its horizontal and vertical components using trig. Vertical velocity: 25sin(30) Horizontal velocity: 25cos(30)3: Work out forces on the mass to find vertical and horizontal acceleration using Newton's Second Law No air resistance so gravity is the only force Vertical acceleration = mg = 1*9.8 = 9.8 ms-2 Horizontal acceleration = 0 ms-24: Use SUVAT equations with the vertical components of velocity and acceleration to find the time the mass is in the air s=ut+1/2 at2 where s = 0, u= 25sin(30) and a=-9.8ms-2 (negative because working in the oppposite direction to the initial , velocity) t=2.55 s5: Use the time in the air and SUVAT to find the horizontal distance travelled s=ut+1/2 at2 where u=25cos(30), t=2.55s and a=0 s=55.2m
Related Maths A Level answers
All answers ▸A ball is kicked and has an instantaneous velocity of 19.6m/s at an angle of 30 degrees to the horizontal. A target lies flat on the ground in the direction the ball is kicked and lies at a distance of (98/5)*(3^1/2)m. Does the ball land on the target?
Find the sum of the first n odd numbers, 1+ 3 + … + 2n-1, in terms of n. What might a mathematician’s thought process be?
Find the derivative of the following function: f(x) = x(x^3 + 2x)
A curve is defined by parametric equations: x = t^(2) + 2, and y = t(4-t^(2)). Find dy/dx in terms of t, hence, define the gradient of the curve at the point where t = 2.