A polystyrene component must not fail when a tensile stress of 1.25 MPa (180 psi) is applied. Determine the maximum allowable su
rface crack length if the surface energy of polystyrene is 0.50 J/m2 (2.86 103 in.-lbf/in.2 ). Assume a modulus of elasticity of 3.0 GPa (0.435 106 psi).
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Emily throws the ball at 30 degree below the horizontal
so here the speed is 14 m/s and hence we will find its horizontal and vertical components
vertical distance between them
now we will use kinematics in order to find the time taken by the ball to reach at Allison
here acceleration is due to gravity
now we will have
now solving above quadratic equation we have
now in order to find the horizontal distance where ball will fall is given as
here it shows that horizontal motion is uniform motion and it is not accelerated so we can use distance = speed * time
so the distance at which Allison is standing to catch the ball will be 5.33 m
We use the kinematic equations,
(A)
(B)
Here, u is initial velocity, v is final velocity, a is acceleration and t is time.
Given, ,
and
.
Substituting these values in equation (B), we get
.
Therefore from equation (A),
Thus, the magnitude of the boat's final velocity is 10.84 m/s and the time taken by boat to travel the distance 280 m is 51.63 s