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take the reciprocals of the indices; this gives ∞, ∞, and 1/2. Thus, the (002) plane parallels both x- and y-axes, and intercepts the z-axis at c/2, as indicated in the drawing. 3.30 (a) We are asked for the indices of the two directions sketched in the figure. For direction 1, the projection on the x-axis is zero (since it lies in the y-z plane), while projections on the y- and z-axes are b/2 and c, respectively. This is an [012] direction as indicated in the summary below x…

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between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. 3.5. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! EXECUTE: v = 2btiˆ + 3ct 2 ˆj . vx = v y gives t = 2b 3c . ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component…

between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

between 0 and 2.0 s, calculate x and y and plot y versus x. Figure 3.3b 3.4. EVALUATE: The sketch shows that the instantaneous velocity at any t is tangent to the trajectory. ! ! IDENTIFY: v = dr/dt . This vector will make a 45° -angle with both axes when its x- and y-components are equal. d (t n ) SET UP: = nt n −1 . dt ! ˆ EXECUTE: v = 2bti + 3ct 2 ˆ . vx = v y gives t = 2b 3c . j ! EVALUATE: Both components of v change with t. IDENTIFY and SET UP: Use Eq.(3.8) in component form to…

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